Here's the scenario, in a nutshell:
(1) Sent by the church in Antioch, Barnabas & Paul deliver financial relief in advance of the prophesied famine, so the Jerusalem church can begin buying extra and stocking up before food becomes scarce. Arriving during an outbreak of persecution, at the Passover of 44 AD (Acts 12), Paul & Barnabas are unable to meet with the church, which has gone into hiding.
(2) Commissioned by the Holy Spirit in 44 or 45 AD Barnabas & Paul go on to plant four churches in Southern Galatia (A.13-14), returning to Antioch by 47 or 48 AD.
(3) The famine now over, Peter comes to visit Antioch in late 48 or early 49 (G.2:10) but so do some from Judea's circumcision party, "certain men from James" (G.2:11, A.15:1) and these 'Judaizers' create social schism among the church. Soon Peter is swayed (G.2:12) and even Barnabas is led astray (G.2:13). Paul rebukes Peter (G.2:11ff) and Barnabas rejoins Paul's side in the ongoing debate (A.15:2).
(4) The church in Antioch kicks the debate 'up' to Jerusalem (A.15:2-3) where Paul, Barnabas & Titus win the day on the big issue, but accept James' conditions. That is, the delegation accepts them. Barnabas & Titus may have outvoted Paul on this; Paul's contempt for Jerusalem's three laws becomes evident soon enough.
(5) P,B & T return to Antioch, still in 49 AD. Before long, Barnabas takes John Mark to Cyprus, after which Paul receives word that some 'Judaizers' from Antioch had gone on to cause trouble in Galatia - evidently during the time of Jerusalem's council.
(6) Paul writes a scathing letter without Barnabas' balancing influence, both asserting Jerusalem's official countenance of his Gospel AND revealing his own harsh opinions about Jerusalem's attitudes in general. Finally, Titus & Luke deliver the letter, visit with the churches (G.2:3), and testify about events in Antioch & Jerusalem, probably saving Jerusalem's letter to present as a last resort.
(7) Titus & Luke proceed to their prearranged rendezvous point at 'Troy' (Troas, A.16:8). Paul & Silas lag long enough for each Galatian church to digest their visit from Luke & Titus, and then proceed to discover at least three of the churches doing fairly well, in part thanks to Timothy (A.16:1-2). By now it is early/mid 50 AD.
Without defending it here, that's the basic scenario. Galatians was Paul's first epistle, written to the four churches of South Galatia, but not until AFTER the Council of Acts 15.
Now, ask me some challenging questions!