"...Paul confronted Peter about his error of retreating from the Gentiles when the Judaizers showed up...."
What is a 'Judaizer'? A 'God-Fearer' one who sympathized, with and practiced as far as possible, the Law of Moses, yet, not having been born in any of the twelve tribes, remained an gentile nevertheless? And when Peter retreated from his stance re: these gentiles was not at the insistence of James and his followers who grudgingly admitted the validity of the God-Fearers, but only as auxiliary to, not bona fide members of God's chosen people?
"...Paul said he was sent to the Jews with the Gospel..."
By 'gospel' do you mean Paul was sent 'to the Jews' to proclaim the fulfillment of Daniel's prophecy? To all the Jews?
The “error” is according to that which is actually true. For example, if I think Paul was an African-American and taught this, according to what is actually true, I am wrong. However, I might still be a believer.
Your next statements puzzle me a little. The Judaizers were Jewish men (yes, bona fide blood members of God’s physically chosen people, the Jews), who followed Paul around telling folks that Jesus was fine, but there was more to the Gospel than just trusting Jesus to forgive your sins. They taught you now had the “equipment” to really obey the Law of Moses and thereby insure your salvation. This confusion of the Gospel became a great source of irritaion to Paul. Read the entire letter to the Galations and listen to how angry Paul is that such men would attempt to water down the message.
“Even if we or an angel from heaven should preach a gospel other than the one we preached to you, let him be eternally condemned.” Do I read that, “Go to hell”? Sure, this is language intended to shake them up. But, the message is the same. There is one message about Jesus being adequate without cermonial additions.
And what I meant is that Paul recognized that Peter, while sadly mistaken about his pulling back, was still a “sent one” (apostle) to the Jews to tell them that their Messiah had come. As far as Daniel’s prophecy points toward this, yes, Peter was sent to all Jews to tell them about Jesus. And, oddly, Peter was the first one who really saw the breaking down of the barrier between the Jews and Gentiles (Acts 10:9ff).