The account St Paul gives of his confrontation with St Peter in Antioch (Gal. 2:11-21) is well-known, especially in Protestant circles; it seems to show the superiority of Paul's understanding of the Gospel, over against that of Peter and of James. That is, the "Pillars" of the Church (2:9) were wrong in their way of practice, effectively separating Jews and Gentiles in the table fellowship (which includes the possibility of Eucharistic division), where no such separation was warranted. Fascinating, though, is that this story is not recorded in the narrative of Acts (even though Sts Luke and Paul were traveling companions) nor does Paul himself give the conclusion of the event in Galatians. This creates two problems worth investigating: when did the confrontation happen within the timeline set by Acts and how was it resolved (if indeed, it was)?
The Apostle sets a rough timeline in the Galatian epistle itself, based on the events in Acts 9: after he received his call in Damascus (9:15 cf. Gal. 1:16) and began to proclaim the Gospel there ("immediately he preached..., 9:20), he went to Arabia for an undetermined amount of time because of persecution (9:23-25). Later, he returned to Damascus (Gal. 1:17): it is difficult to say whether his stay in Arabia and his return to Damascus and subsequent tenure there, or just the latter, is what he means by the "three years" he waited to go to Jerusalem (1:18).
At this point, the narratives get a little confused with the terminology: I'll risk a little anachronism and take Paul's account as a clarification/correction to Luke's account. In Acts, Paul unsuccessfully tries to present himself to the disciples in Jerusalem (9:26); it is only through the mediation of St Barnabus that he gains an audience with "the apostles" (9:27) and begins to dispute, curiously enough, with the Greek-speaking (Diasporan) Jews (9:29), which causes "the brethren" to send him out through Caesarea towards Tarsus. In his epistle, Paul elides over any trouble getting an audience and any help from Barnabus, insisting that he only saw Sts Peter and James and "was unknown by face to the churches of Judaea" (Gal 1:18-23). He does, after that, go to "Syria and Cilicia," in which he would have found the city of Tarsus. Of note is that, in the midst of this narrative, St Paul affirms his truth-telling: "Now, about the things I write to you...indeed, before God, I do not lie." Why would he have included this statement, unless the narrative itself was publicly being doubted?
How do these narratives fit together? In chapter 2 of the epistle, St Paul says that he "again went up to Jerusalem," this time with Barnabus, this time to meet "those of reputation" whom he later calls "Pillars," and has a rough time with those "who came in by stealth to spy out our liberty which we have in Christ Jesus" (vv. 1-10). It seems, then, that a plausible timeline looks like this:
Saul's conversion/call and initial preaching: Acts 9:1-25
Arabia and then back to Damascus: Gal. 1:17
~3 years elapse
First trip to Jerusalem: unrecorded in Acts, Gal. 1:18-24
First trip to Syria and Cilicia: Gal. 1:21
14 years elapse
Second trip to Jerusalem: Acts 9:26-30 and Gal. 2:1-10
(This means that those who had come into to "spy out our liberty" are the "Hellenists" with whom he disputed in Jerusalem. It is curious, then, that the Gentiles converts (Acts 6:1, yet cf. 11:20) -- were more stringent about Torah-observance than the Jewish Christians were. As Paul notes in Galatians, the "Pillars" were fine not circumcising Titus.)
Second trip to Syria and Cilicia: Acts 9:30
Peter's vision and the conversion of Cornelius: Acts 10
Paul's arrival in Antioch: Acts 11:19
Here is the most curious part. The conflict between Peter and Paul in Antioch cannot occur until after Paul arrives there, and is at least somewhat settled, which happens in Acts 11:26. Yet, in earlier in that same chapter (11:2-3), Peter defends eating with the "uncircumcised," causing the "those of the circumcision" (the Jewish Christians) to say "Then God has also granted to the Gentiles repentance to life" (11:18). Why, then, does Peter fall into such great error in Antioch? It is worth noting, I think, that Peter is ok eating with the Gentiles until "men came from James" (Gal. 2:12), that is, folks from the predominantly Jewish Jerusalem church, who would be more likely to be Torah-observant, and who had folks "among them" that Paul had already contended with about circumcision.
It seems likely -- and the number of years is indeterminable -- that the conflict with Peter happened right before the Jerusalem Council. In the beginning of Acts 15, Luke says: "And certain men came down from Judaea and taught the brethren [in Antioch, cf. 14:26-28], 'Unless you are circumcised according to the custom of Moses, you cannot be saved.' Therefore, when Paul and Barnabus had no small dissension and dispute, they determined that Paul and Barnabus and certain others of them should go up to Jerusalem, to the apostles and the elders, about this question" (vv. 1-2). After Acts 12 we are not told the whereabouts or travels of St Peter; it is quite possible he traveled to Antioch during that time, when Sts Paul and Barnabus were evangelizing the Galatians (in Antioch of Pisidia: Acts 13). When they returned and had "stayed there a long time with the disciples," eating and drinking in the Lord, then came the rabble-rousers. Since they came "down from Judaea," they are equated with "men from James." "From James" here functions as a circumlocution for "out of Jerusalem" -- it does not necessarily mean that they were on official business from the bishop; rather, it seeks to set them apart from non-believing Jews of Judaea -- they were members of good-standing in the Jerusalem church, yet what they preached ended up being "another Gospel" (Gal. 1:6). Not only did they cause Peter to withdraw from (possibly) Eucharistic fellowship with the Gentile believers, but they began to preach the necessity of circumcision. This is why Paul is so strident about the topic in the epistle: what he had successfully combated at Antioch in Syria, even straightening out an Apostle of the Lord, was now being preached and believed in Antioch of Pisidia.
If this reconstruction is right, the resolution of the confrontation is the repentance of Peter. When he speaks up in the Council, his words not only recall his experience with Cornelius but also are reminiscent of what Paul records himself as saying in the Antiochean confrontation: "we believe that through the grace of the Lord Jesus Christ we shall be saved in the same manner as they" (Acts 15:11) that is, "we have believed in Christ Jesus, that we might be justified by faith in Christ and not by works of the law; for by the works of the law no flesh shall be justified" (Gal. 2:16).
This also means that the epistle is most likely written after the Jerusalem Council (it could, conceivably, be written on the way to the Council). Paul's reaction to the Council's decrees, as recorded in Acts, become an important interpretive grid for the epistle itself:
"Then it pleased the apostles and elders, with the whole church, to send chosen men of the own company to Antioch with Paul and Barnabus...when they were sent off, they came to Antioch: and when they had gathered the multitude together, they delivered the letter. When they had read it, they [the multitude] rejoiced over its encouragement" (15:22, 30-31).
"And as they [Paul and Silas, cf. 15:40] went through the cities [in the region of Galatia!], they delivered to them the decrees to keep, which were determined by the apostles and elders at Jerusalem. So the churches were strengthened in the faith, and increased in number daily" (16:4-5).
This means that Galatians, even though it is the paragon of seeming "anti-Torah" sentiment, cannot be properly read that way, as Acts sets the proper historical and ecclesial context. Rather, Paul's strong words about the Law are against those Hellenists and Judaizers that would go beyond the Apostolic Decree of the Jerusalem Council and add more than the four ritual requirements found therein. Paul himself had delivered those decrees to the Galatians, making them part of the Gospel which he had preached there. All of this allows us to read Galatians (dare I say it?) afresh, not producing a hard-and-fast dichotomy between faith and works, but a necessary one against Judaizers and the Gospel.