Peter's vision was to affirm to him that God wanted them to minister God's grace to all people.
Gal 2:9 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.
(Of course when you look at the context of those three verses, the meaning is further amplified)
But the fact of the matter is that the ministry of Paul and Barnabas only came AFTER God gave Peter his vision, when Cornelius was converted, when Peter communicated his vision, and after the Church in Antioch was in a period of prayer and fasting. Only after that, did the the Holy Spirit say, "Set apart for me Barnabas and Saul for the work to which I have called them." (Acts 13:2).
Nothing you have said nullifies any of the arguments I presented above. The point is that Paul, in fact, did go on his missionary journeys to the nations; if not for the vision provided to Peter, it simply wouldn't have happened.
Why does it matter which happened first? God is the one who is in control, not Peter. He set it in motion by giving Peter the vision.