Salam
The Quran has a definition which even a disbelieving wife can be included in the term "family" of a Prophet:
فَنَجَّيْنَاهُ وَأَهْلَهُ أَجْمَعِينَ | So We delivered him and all his family, | Ash-Shu'araa : 170
إِلَّا عَجُوزًا فِي الْغَابِرِينَ | except an old woman who remained behind. | Ash-Shu'araa : 171
ثُمَّ دَمَّرْنَا الْآخَرِينَ | Then We destroyed [all] the rest, | Ash-Shu'araa : 172
From another angle, Lut (a) who is a nephew of Ibrahim (a), belongs to the chosen family of the time and who unrighteous cannot be included in his family:
قَالَ يَا نُوحُ إِنَّهُ لَيْسَ مِنْ أَهْلِكَ ۖ إِنَّهُ عَمَلٌ غَيْرُ صَالِحٍ ۖ فَلَا تَسْأَلْنِ مَا لَيْسَ لَكَ بِهِ عِلْمٌ ۖ إِنِّي أَعِظُكَ أَنْ تَكُونَ مِنَ الْجَاهِلِينَ | Said He, ‘O Noah! Indeed, He is not of your family. Indeed, he is [personification of] unrighteous conduct. So do not ask Me [something] of which you have no knowledge. I advise you lest you should be among the ignorant.’ | Hud : 46
Sarah (a) is a chosen lady that belongs to an Ahlulbayt of her time and so does the first Mariam (a), even though the latter is not a mother of chosen guides. So the criteria of being a mother of chosen is not really there and sort of almost made up by Shiites. However, what does the family mean in terms of the one unrighteous don't belong to, the Quran further shows, not only are they all righteous, but that they are in fact all chosen:
إِنَّ اللَّهَ اصْطَفَىٰ آدَمَ وَنُوحًا وَآلَ إِبْرَاهِيمَ وَآلَ عِمْرَانَ عَلَى الْعَالَمِينَ | Indeed Allah chose Adam and Noah, and the family of Abraham and the family of Imran above all the nations; | Aal-i-Imraan : 33
As this is held and elaborated by Quran, to see it not pertain to us, would be foolish. Why elaborate a concept with no relevance?
Now in Surah Ahzab, there is two places that we can see more context to the flow of 33:33. One is the Salawat verse is right after what?
لَا جُنَاحَ عَلَيْهِنَّ فِي آبَائِهِنَّ وَلَا أَبْنَائِهِنَّ وَلَا إِخْوَانِهِنَّ وَلَا أَبْنَاءِ إِخْوَانِهِنَّ وَلَا أَبْنَاءِ أَخَوَاتِهِنَّ وَلَا نِسَائِهِنَّ وَلَا مَا مَلَكَتْ أَيْمَانُهُنَّ ۗ وَاتَّقِينَ اللَّهَ ۚ إِنَّ اللَّهَ كَانَ عَلَىٰ كُلِّ شَيْءٍ شَهِيدًا | There is no sin on them [in socializing freely] with their fathers, or their sons, or their brothers, or their brothers’ sons, or the sons of their sisters, or their own womenfolk, or what their right hands own. And be wary of Allah. Indeed Allah is witness to all things. | Al-Ahzaab : 55
The bold is female plural and addressed at the wives, then this verse comes up:
إِنَّ اللَّهَ وَمَلَائِكَتَهُ يُصَلُّونَ عَلَى النَّبِيِّ ۚ يَا أَيُّهَا الَّذِينَ آمَنُوا صَلُّوا عَلَيْهِ وَسَلِّمُوا تَسْلِيمًا | Indeed Allah and His angels bless the Prophet; O you who have faith! Invoke blessings on him and invoke Peace upon him in a worthy manner. | Al-Ahzaab : 56
So we see the status of the Prophet (s) relates to why God is emphasizing on the wives to fear him, while everyone should fear God, they should be extra fearful, due to who they are married to.
The other place is verses 33:6-8:
النَّبِيُّ أَوْلَىٰ بِالْمُؤْمِنِينَ مِنْ أَنْفُسِهِمْ ۖ وَأَزْوَاجُهُ أُمَّهَاتُهُمْ ۗ وَأُولُو الْأَرْحَامِ بَعْضُهُمْ أَوْلَىٰ بِبَعْضٍ فِي كِتَابِ اللَّهِ مِنَ الْمُؤْمِنِينَ وَالْمُهَاجِرِينَ إِلَّا أَنْ تَفْعَلُوا إِلَىٰ أَوْلِيَائِكُمْ مَعْرُوفًا ۚ كَانَ ذَٰلِكَ فِي الْكِتَابِ مَسْطُورًا | The Prophet is Awla to the faithful than their own souls, and his wives are their mothers and the blood relative, some of them are Awla then others in the book of God, from the believers and emigrants, only that you should towards your Awliya do goodness, that has been written in the Book. | Al-Ahzaab : 6
وَإِذْ أَخَذْنَا مِنَ النَّبِيِّينَ مِيثَاقَهُمْ وَمِنْكَ وَمِنْ نُوحٍ وَإِبْرَاهِيمَ وَمُوسَىٰ وَعِيسَى ابْنِ مَرْيَمَ ۖ وَأَخَذْنَا مِنْهُمْ مِيثَاقًا غَلِيظًا | And when We took a pledge from the prophets, and from you and from Noah and Abraham and Moses and Jesus son of Mary, and We took from them a solemn pledge, | Al-Ahzaab : 7
لِيَسْأَلَ الصَّادِقِينَ عَنْ صِدْقِهِمْ ۚ وَأَعَدَّ لِلْكَافِرِينَ عَذَابًا أَلِيمًا | so that He may question the truthful concerning their truthfulness. And He has prepared for the faithless a painful punishment. | Al-Ahzaab : 8
Per hadiths of Imams (a) verse 33:6 is about the Welayat of Ahlulbayt (a), that each will inherit the leadership one by one. The Awliya is in context of what? It's in the context of the same Welayat of the Nabi (a), which the Ulul-Arham some have more of it then others, mainly, the Imam of time is to lead and be referred to, then others when their time comes.
So now let's look at Ayat tatheer:
وَقَرْنَ فِي بُيُوتِكُنَّ وَلَا تَبَرَّجْنَ تَبَرُّجَ الْجَاهِلِيَّةِ الْأُولَىٰ ۖ وَأَقِمْنَ الصَّلَاةَ وَآتِينَ الزَّكَاةَ وَأَطِعْنَ اللَّهَ وَرَسُولَهُ ۚ إِنَّمَا يُرِيدُ اللَّهُ لِيُذْهِبَ عَنْكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا | And stay in your houses and do not flaunt your finery like the former [days of pagan] ignorance and Maintain the prayer and pay the zakat, and obey Allah and His Messenger. Indeed Allah desires to repel all impurity from you, O People of the Household, and purify you with a thorough purification. | Al-Ahzaab : 33
This can be saying to the wives, they are married to a person who God has repelled all uncleanness from and wishes to purify a thorough purification and so this is why God is emphasizing to them. There also something else to consider, that reputation of purity is forbidden except for God to do so. That is people are not to attribute purity to themselves. God on other hand manifests who is pure and who is not. It maybe that this saying the intention of revealing Quran and sending Mohammad (s) even though it talks about purity of past Ahlulbayts, is in fact, to really make all uncleanness gone in the minds of people regarding Ahlulbayt and to make them have an ultimate purity status.
That is one possible meaning, another, can be the Inama limits what God desires to keep away from Ahlulbayt souls to be only uncleanness for the first part, and for the second part it means they are singled out for a ultimate purification.
Now in Arabic, when words are doubled up, it means it's an ultimate form. So when Quran says "if the earth is shaken a shaking", it's not just repeating the word, but meaning, it's ultimate type shaking. If it's not referring to that, it refers to the fact they are all purified a single purification. Both are possible.
Now lets for sake of proving by contradiction, assume it includes the wives and say the Inama refers to what God intended by such commands.
(1) Does it make sense to emphasize they God wants to purify them a ultimate purity with an "Inama"? It would diminish the status of the favor ultimate purity, so that already does not make sense. And them purified a single purification that the Nabi (s) is purified also doesn't make sense to diminish that with the "Inama".
(2) Both meanings, ultra purity or a single purity, is too high status for the wives. That is because Mohammad (s) is way above them, but is this true with Ali (a) and Fatima (a) and holy chosen souls?
(3) If it refers to wives included, it would make all talk of chosen family in the Quran meaningless, and make the Quran emphasize and elaborate something with no relevance to us.
So each of these points, make it abundantly clear, that wives are not included. I will mention one more.
(4) The wives if they obey God are promised honorable Risq in both worlds and heaven. It doesn't make sense to say God only wishes to purify them by these commands either nor address rest of relatives of Nabi (a) and say that to them via the wives.
The term Ahlulbayt is a holy term in the Quran used to emphasize on succession. That Prophets come in groups. They don't come alone.
The hadiths of Mubahila and kisa are also good proofs.
The Quran has a definition which even a disbelieving wife can be included in the term "family" of a Prophet:
فَنَجَّيْنَاهُ وَأَهْلَهُ أَجْمَعِينَ | So We delivered him and all his family, | Ash-Shu'araa : 170
إِلَّا عَجُوزًا فِي الْغَابِرِينَ | except an old woman who remained behind. | Ash-Shu'araa : 171
ثُمَّ دَمَّرْنَا الْآخَرِينَ | Then We destroyed [all] the rest, | Ash-Shu'araa : 172
From another angle, Lut (a) who is a nephew of Ibrahim (a), belongs to the chosen family of the time and who unrighteous cannot be included in his family:
قَالَ يَا نُوحُ إِنَّهُ لَيْسَ مِنْ أَهْلِكَ ۖ إِنَّهُ عَمَلٌ غَيْرُ صَالِحٍ ۖ فَلَا تَسْأَلْنِ مَا لَيْسَ لَكَ بِهِ عِلْمٌ ۖ إِنِّي أَعِظُكَ أَنْ تَكُونَ مِنَ الْجَاهِلِينَ | Said He, ‘O Noah! Indeed, He is not of your family. Indeed, he is [personification of] unrighteous conduct. So do not ask Me [something] of which you have no knowledge. I advise you lest you should be among the ignorant.’ | Hud : 46
Sarah (a) is a chosen lady that belongs to an Ahlulbayt of her time and so does the first Mariam (a), even though the latter is not a mother of chosen guides. So the criteria of being a mother of chosen is not really there and sort of almost made up by Shiites. However, what does the family mean in terms of the one unrighteous don't belong to, the Quran further shows, not only are they all righteous, but that they are in fact all chosen:
إِنَّ اللَّهَ اصْطَفَىٰ آدَمَ وَنُوحًا وَآلَ إِبْرَاهِيمَ وَآلَ عِمْرَانَ عَلَى الْعَالَمِينَ | Indeed Allah chose Adam and Noah, and the family of Abraham and the family of Imran above all the nations; | Aal-i-Imraan : 33
As this is held and elaborated by Quran, to see it not pertain to us, would be foolish. Why elaborate a concept with no relevance?
Now in Surah Ahzab, there is two places that we can see more context to the flow of 33:33. One is the Salawat verse is right after what?
لَا جُنَاحَ عَلَيْهِنَّ فِي آبَائِهِنَّ وَلَا أَبْنَائِهِنَّ وَلَا إِخْوَانِهِنَّ وَلَا أَبْنَاءِ إِخْوَانِهِنَّ وَلَا أَبْنَاءِ أَخَوَاتِهِنَّ وَلَا نِسَائِهِنَّ وَلَا مَا مَلَكَتْ أَيْمَانُهُنَّ ۗ وَاتَّقِينَ اللَّهَ ۚ إِنَّ اللَّهَ كَانَ عَلَىٰ كُلِّ شَيْءٍ شَهِيدًا | There is no sin on them [in socializing freely] with their fathers, or their sons, or their brothers, or their brothers’ sons, or the sons of their sisters, or their own womenfolk, or what their right hands own. And be wary of Allah. Indeed Allah is witness to all things. | Al-Ahzaab : 55
The bold is female plural and addressed at the wives, then this verse comes up:
إِنَّ اللَّهَ وَمَلَائِكَتَهُ يُصَلُّونَ عَلَى النَّبِيِّ ۚ يَا أَيُّهَا الَّذِينَ آمَنُوا صَلُّوا عَلَيْهِ وَسَلِّمُوا تَسْلِيمًا | Indeed Allah and His angels bless the Prophet; O you who have faith! Invoke blessings on him and invoke Peace upon him in a worthy manner. | Al-Ahzaab : 56
So we see the status of the Prophet (s) relates to why God is emphasizing on the wives to fear him, while everyone should fear God, they should be extra fearful, due to who they are married to.
The other place is verses 33:6-8:
النَّبِيُّ أَوْلَىٰ بِالْمُؤْمِنِينَ مِنْ أَنْفُسِهِمْ ۖ وَأَزْوَاجُهُ أُمَّهَاتُهُمْ ۗ وَأُولُو الْأَرْحَامِ بَعْضُهُمْ أَوْلَىٰ بِبَعْضٍ فِي كِتَابِ اللَّهِ مِنَ الْمُؤْمِنِينَ وَالْمُهَاجِرِينَ إِلَّا أَنْ تَفْعَلُوا إِلَىٰ أَوْلِيَائِكُمْ مَعْرُوفًا ۚ كَانَ ذَٰلِكَ فِي الْكِتَابِ مَسْطُورًا | The Prophet is Awla to the faithful than their own souls, and his wives are their mothers and the blood relative, some of them are Awla then others in the book of God, from the believers and emigrants, only that you should towards your Awliya do goodness, that has been written in the Book. | Al-Ahzaab : 6
وَإِذْ أَخَذْنَا مِنَ النَّبِيِّينَ مِيثَاقَهُمْ وَمِنْكَ وَمِنْ نُوحٍ وَإِبْرَاهِيمَ وَمُوسَىٰ وَعِيسَى ابْنِ مَرْيَمَ ۖ وَأَخَذْنَا مِنْهُمْ مِيثَاقًا غَلِيظًا | And when We took a pledge from the prophets, and from you and from Noah and Abraham and Moses and Jesus son of Mary, and We took from them a solemn pledge, | Al-Ahzaab : 7
لِيَسْأَلَ الصَّادِقِينَ عَنْ صِدْقِهِمْ ۚ وَأَعَدَّ لِلْكَافِرِينَ عَذَابًا أَلِيمًا | so that He may question the truthful concerning their truthfulness. And He has prepared for the faithless a painful punishment. | Al-Ahzaab : 8
Per hadiths of Imams (a) verse 33:6 is about the Welayat of Ahlulbayt (a), that each will inherit the leadership one by one. The Awliya is in context of what? It's in the context of the same Welayat of the Nabi (a), which the Ulul-Arham some have more of it then others, mainly, the Imam of time is to lead and be referred to, then others when their time comes.
So now let's look at Ayat tatheer:
وَقَرْنَ فِي بُيُوتِكُنَّ وَلَا تَبَرَّجْنَ تَبَرُّجَ الْجَاهِلِيَّةِ الْأُولَىٰ ۖ وَأَقِمْنَ الصَّلَاةَ وَآتِينَ الزَّكَاةَ وَأَطِعْنَ اللَّهَ وَرَسُولَهُ ۚ إِنَّمَا يُرِيدُ اللَّهُ لِيُذْهِبَ عَنْكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا | And stay in your houses and do not flaunt your finery like the former [days of pagan] ignorance and Maintain the prayer and pay the zakat, and obey Allah and His Messenger. Indeed Allah desires to repel all impurity from you, O People of the Household, and purify you with a thorough purification. | Al-Ahzaab : 33
This can be saying to the wives, they are married to a person who God has repelled all uncleanness from and wishes to purify a thorough purification and so this is why God is emphasizing to them. There also something else to consider, that reputation of purity is forbidden except for God to do so. That is people are not to attribute purity to themselves. God on other hand manifests who is pure and who is not. It maybe that this saying the intention of revealing Quran and sending Mohammad (s) even though it talks about purity of past Ahlulbayts, is in fact, to really make all uncleanness gone in the minds of people regarding Ahlulbayt and to make them have an ultimate purity status.
That is one possible meaning, another, can be the Inama limits what God desires to keep away from Ahlulbayt souls to be only uncleanness for the first part, and for the second part it means they are singled out for a ultimate purification.
Now in Arabic, when words are doubled up, it means it's an ultimate form. So when Quran says "if the earth is shaken a shaking", it's not just repeating the word, but meaning, it's ultimate type shaking. If it's not referring to that, it refers to the fact they are all purified a single purification. Both are possible.
Now lets for sake of proving by contradiction, assume it includes the wives and say the Inama refers to what God intended by such commands.
(1) Does it make sense to emphasize they God wants to purify them a ultimate purity with an "Inama"? It would diminish the status of the favor ultimate purity, so that already does not make sense. And them purified a single purification that the Nabi (s) is purified also doesn't make sense to diminish that with the "Inama".
(2) Both meanings, ultra purity or a single purity, is too high status for the wives. That is because Mohammad (s) is way above them, but is this true with Ali (a) and Fatima (a) and holy chosen souls?
(3) If it refers to wives included, it would make all talk of chosen family in the Quran meaningless, and make the Quran emphasize and elaborate something with no relevance to us.
So each of these points, make it abundantly clear, that wives are not included. I will mention one more.
(4) The wives if they obey God are promised honorable Risq in both worlds and heaven. It doesn't make sense to say God only wishes to purify them by these commands either nor address rest of relatives of Nabi (a) and say that to them via the wives.
The term Ahlulbayt is a holy term in the Quran used to emphasize on succession. That Prophets come in groups. They don't come alone.
The hadiths of Mubahila and kisa are also good proofs.