I have to add there is a lot of assuming there are two Gospels in Acts. We do not have an account of Peter, James and others submitting to Paul. At the Jerusalem council all were unified in Peters proclamation that the Gentiles received Christ the same way they did.
"But contrariwise, when they saw that the GOSPEL OF THE UNCIRCUMCISION was COMMITTED UNTO ME, as the GOSPEL OF THE CIRCUMCISION was UNTO PETER: (For he that wrought effectually in Peter to the APOSTLESHIP OF THE CIRCUMCISION, the same was MIGHTY IN ME TOWARD THE GENTILES:)" Gal. 2:7,8.
"And when James, Cephas, and John, who seemed to be pillars, PERCEIVED the GRACE THAT WAS GIVEN UNTO ME, they gave to me and Barnabas the right hands of fellowship; that WE should GO UNTO THE HEATHEN, and THEY UNTO THE CIRCUMCISION". Gal. 2:9.