Where was Paul's grace in dealing with Peter?

From what I have seen, even a public error stands more chance of being corrected by the perpetrator if he or she is first approached privately. Besides, if the 'corrector' is the one wrong, that saves a lot of public embarrassment!

 

If we look at the facts, then we find that Paul was acting exactly like he should have. He was protecting those who had been entrusted to his leadership. Peter's actions caused even Barnabas to be led astray. I am certain this caused Paul to go balistic, in a holy way. Paul knew what it was like to be obedient to the law, and he knew what it was like to walk in the freedom that Jesus Christ offers. When he saw Peter leading the way back into the law, he gave a great rebuke to a fellow apostle. The great thing is that Peter, when writing, says good things about Paul.

GAL 2:11 When Peter came to Antioch, I opposed him to his face, because he was clearly in the wrong. 12 Before certain men came from James, he used to eat with the Gentiles. But when they arrived, he began to draw back and separate himself from the Gentiles because he was afraid of those who belonged to the circumcision group. 13 The other Jews joined him in his hypocrisy, so that by their hypocrisy even Barnabas was led astray.
GAL 2:14 When I saw that they were not acting in line with the truth of the gospel, I said to Peter in front of them all, "You are a Jew, yet you live like a Gentile and not like a Jew. How is it, then, that you force Gentiles to follow Jewish customs?
GAL 2:15 "We who are Jews by birth and not `Gentile sinners' 16 know that a man is not justified by observing the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by observing the law, because by observing the law no one will be justified.
GAL 2:17 "If, while we seek to be justified in Christ, it becomes evident that we ourselves are sinners, does that mean that Christ promotes sin? Absolutely not! 18 If I rebuild what I destroyed, I prove that I am a lawbreaker. 19 For through the law I died to the law so that I might live for God. 20 I have been crucified with Christ and I no longer live, but Christ lives in me. The life I live in the body, I live by faith in the Son of God, who loved me and gave himself for me. 21 I do not set aside the grace of God, for if righteousness could be gained through the law, Christ died for nothing!"