Yeah, I think people must commonly assume it is actually something recommended in the Qur'an, but it doesn't seem to be recommended at all, nor is there even this notion really present about how certain things that a relative does can increase or decrease the status or prestige of the family members or in the view of God even. Plus, murder or killing as a punishment is exclusively for enemy combatants who are attacking and murderers (and can also be forgiven as well or not killed), and there is no stoning to death mentioned in the Qur'an or beheading, or mutilation, or genital mutilation, not even circumcision as far as I am aware, none of it appears in the Qur'an, but a lot of it does appear in the Bible, and it is possible that people inspired by such things brought it into the Islamic cultures or something, but it doesn't appear in the Qur'an at least. What the Qur'an does have is stuff that can be paraphrased as "if someone tries to kill you in war or attacks you violently with an intent to kill, no need to let them kill you or loved ones, but defend yourself, strike back, feel free to do whatever is reasonable to survive and end the threat" which sounds fine and just basic human nature to me anyway, and it asks that people don't go nuts or into overkill mode or transgress or go too far in their spree, and never to harm the innocent or non-combatants or indirect people which is all criminal and evil sort of conduct, so it sounds pretty reasonable and just to me, there is no sins of the father pass to the son sort of business or that if your kid is evil then you should be punished or shamed for it.
There is a lot of good stuff, if people followed the Qur'an closely and other influenced weren't present and allowed in as much as they were, one might have seen a very different sort of picture of the religion than exists today, though I still believe it is more than likely that it would be considered just as despicable and hated, and also most likely used for evil ends by evil people anyway, as is practically anything always.
The Qur'an also suggests the punishment of lashings of a certain number for people who are proven by testimony and authenticated witnesses, evidence, and proof, for adulterers, and then the adulterers are mercifully left alone and allowed to even be with each other as far as what the Qur'an seems to say, so it amounts to a serious spanking (maybe they like it), but it does suggest to make sure you do it hard enough so that it doesn't just act as a merely symbolic lashing, so probably suitable to hand over to a sadist to perform on them, but a sadist controlled by the law, the official government spanker.
One of the punishments people don't like too much these days, is the recommendation of chopping off the hand of a thief, so that people will be terrified of theft or getting caught for theft, and will also be seen from a distance as a potential thief or former thief, but maybe unlikely to steal, unless they are a mental case, which they would be if they are stealing with such harsh rules or their hand already cut off, in which case its likely that they are given some other sort of treatment or containment to prevent them from further trouble-making. Plus, if they are stealing out of need, then it is likely better to have mercy and treat them as a charity case, though I've seen some real rotten thieves, and wouldn't mind if their hands were chopped off, ok fine, just one!
The Qur'an is also against the murder of infants (infanticide) which was commonly practiced in cultures, like even in Greece and possibly Rome, but Ancient Egyptians supposedly didn't like the practice according to Greek accounts. The Arabs supposedly were not too dissimilar from ancient Greco-Romans and Babylonians maybe too or Canaanites before them, and so they were said to commonly murder their infant children at times, but the Qur'an very strictly forbids this, but I don't remember if any punishment for those who do this is mentioned except that they will be judged for it, but its more than likely it was made illegal and harshly prosecuted in Muslim cultures. It says "Do not kill yourselves" and "Do not kill your children" I'm pretty sure, and in so many cases called "Honor Killings" there are people killing their own family members, their own children, which is surely heinous in the sight of the God presented by the Qur'an.
The Bible on the other hand had quite different ideas apparently about such things in comparison to the Qur'an, and insists that people should kill their own children if necessary for certain crimes, like saying "Hey, how about we worship some other God?". The New Testament brings up something like this as well, where Jesus seems to be calling the Jews of the time a bunch of fakers for not murdering their own kids enough.