Peter was never the head of the church at Antioch. Peter's commission was simple. [Matthew 10:5-6] These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: But go rather to the lost sheep of the house of Israel. [Galatians 2:7-8] 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:
Here are two very definitive scriptures showing the commission of the Apostle Peter. Paul was commissioned....basically to everyone....[Acts 9:15] circumcised..... as well as non circumcised. Peter never set foot in Rome and scripture shows him elsewhere.....always evangelizing the Israelites.
The only time scripture shows Peter in Antioch was when he was being chewed out by Paul! [Galatians 2:11] But when Peter was come to Antioch, I withstood him to the face, because he was to be blamed. If you read further (verse 12) you'll see that Peter was frightened of those sent from James in Jerusalem. This is hardly the profile of a "Man in charge"!
The Gospels show that before Jesus ascended, He told the apostles to take His Word to the gentiles and to baptize them in the name of the Father, Son and Holy Spirit.