The Church in the diasporah were not all Gentiles, maybe not even a majority of them until later in the century, as many Jews had already dispersed into cities in the Mediterranean region over time.
You are mistaken. Paul began quite early on deliberately targeting the God-fearers (righteous Gentiles) in the synogogues out in the Empire.
On top of that, Paul met with Peter and the others three times in Acts, all of them being Jews, so one simply cannot in any way dismiss this as just an appeal to Gentiles.
Paul couldn't do just anything he wanted to. He was under James and Peter for example. That doesn't mean Paul's primary mission wasn't to Gentiles.
Also, as you should know, if a male Gentile were to convert into any Jewish branch, he was to be circumcised-- period! The fact that Paul said that doing this would actually be an affront to "the Way" says tons.
Judaism does NOT teach that Gentiles need to become Jews. We teach that Gentiles need only be righteous Gentiles. You guys do not for any reason need to become circumcised and take on the covenant. The early Church agreed with this. Paul agreed with this. It's what the emphasis of every one of his epistles is.
And we know that Jews and Gentiles began to intermarry,
We do? Where in your scriptures does it say this?
Also, if Jesus was just preaching conventional Law then why so many questions addressed to him that includes the hostility we read?
I have addressed this over and over and over in my writings here in this forum. The back and forth between Jesus (of bet Hillel) and the Pharisees of bet Shammai was typical. It was quite normal for the two schools to have these sorts of question and answers sessions, to argue, to have sincere disputes. It was the rage at this time in Jewish history. We have plenty of examples of this in the Talmud. There is nothing exceptional about what happened between Jesus and the other Pharisees.
I would like to recommend the following book by Orthodox Rabbi Harvey Falk: Jesus the Pharisee--A New Look at the Jewishness of Jesus
Actually most scholars I've read believe there were more than two schools.
I don't know about this, and I certainly don't know about "most scholars". Perhaps you are referring to groups beyond the Pharisees such as the Essenes. But the Pharisees themselves, there were only two groups that historically matters: bet Hillel and bet Shammai.
Also, Jesus did not line up with Hillel because Hillel still taught that the letter of the Law was still important to follow, although he did allow more flexibility than the Shammai school did. Obviously, there were other areas of disagreements between them as well.
What makes you think Jesus was against keeping the letter of the law? You have to keep the letter of the law if you are going to keep its spirit.
Finally, in order for Jesus to have even been a footnote in Jewish history,
Jesus is not even a minor footnote in Jewish history. None of his ideas about Torah were original. In a word, he simply didn't contribute anything of not to Judaism. What's worse, his followers took what he said, and perverted it away from an obedience centered thing to a whole theology centered thing to start a new religion that was hostile to his own Judaism.
Put simply, the Twelve gradually walked away from the Law
You never were able to prove this.