... besides if James had authority, why does Paul go to Peter? Clearly it’s James’ people who are influencing people to eat as Jews. Paul doesn’t go to James or his people to tell them not to eat as Jews, but rather goes to Peter, for going along with James.
Why?
Unless Peter has authority over James, Peter could be simply said to be going along to getting along, obeying the passage about not letting any differences cause discord. Paul doesn’t go to James, but instead criticizes Peter for being a hypocrite. A hypocrite, mind you, is someone who proclaims one thing, and behaves in a contrary manner. So in that one word we learn that Peter has proclaimed a doctrine against what would later be called “Judaizing,” and that his offense was his ACTIONS, not heresy (which is the proclamation of false doctrine.)
So Paul sees PETER as the one who is responsible for going along with JAMES, rather than seeing James as responsible. If Peter is responsible, than it is Peter who has authority.
Notice also that Paul doesn’t chastise James’ people, either. It’s not Paul’s place. Paul, instead, urges Peter to do the chastising, because Peter is in charge; Paul is merely serving as an informal advisor to Peter.
Let's not mix our history. There are two stories to consider. The first one was when Paul, Barnabas and Luke were in Antioch, And certain men came down from Judea and taught the brethren, “Unless you are circumcised according to the custom of Moses, you cannot be saved.” (Acts 15:1). The dispute became so great that a bunch of them (including Paul and Barnabas) went to Jerusalem (not Rome) to the Apostles and elders to sort the matter out. It was there that all sides gave their testimony, including corroborating testimony from Peter. James offered a recommendation, and the apostles and elders took it.
The incident between Paul and Peter mentioned by Paul in Galatians is an entirely different story. Peter succumbed to the peer pressure of the Jews who still clung to their old ways. He behaved one way when these folks were around, and another when they weren't. He was a hypocrite. Paul confronted him directly, as the Lord advised in Matthew 18. It has nothing to do with Peter as an authority figure, but with Peter as a fellow believer in error.
Still no pope! However, I've quite enjoyed dialog. You've really brought forth some excellent Scripture.