I am familiar with the Incident of Antioch but not of anything else, if they didnt get along was there a rift between churches that followed Christianity, some that followed James and others that followed Paul.
Hey! Great question.
I'm a moderator at the newly formed /r/AskBibleScholars and I've cross-posted this over there.
Hopefully, one of our Bible scholars will have an answer for you soon.
All we really have that is reliable is Paul's own letters. Paul describes some pretty bitter disagreement with James (as the head of the Jerusalem church) over the necessity of the law for gentile converts (Galatians 2:12, 5:12), particularly circumcision, but ultimately claims that James allowed him to convert gentiles without circumcision in exchange for a donation to the church (Galatians 2:9-10).
Acts is later church propaganda, written no earlier than the late 1st Century. (The Acts Seminar dates it to around 115 CE. See also Richard Pervo's Dating Acts) and is not reliable as history. It appears to have been written specifically to harmonize Pauline (gentile) and Petrine (Jewish) factions of Christianity by making Paul appear more respectful of both the Jerusalem Apostle and the law than he probably really was and by making the Jerusalem Apostles more accepting of Paul's revelation than they probably really were.
It does look like there was hostility between Paul and the Jerusalem church and Paul himself speaks disparagingly of the Jerusalem Apostles (Galatians 2:6, 2 Corinthians 11:5 and Galatians 5:12 where he says he wishes they would cut their own dicks off.