These verses start out with a bang with Paul telling Peter he was clearly in the wrong. What did Peter do? Peter basically tried balancing works with grace. He also didn't want to be with the Gentiles when the Jews showed up. It is classic scenario like when you are with someone and talking with them and then the "cool" people show up so you ditch the person you were talking with because you didn't want to deal with the grief. Peter didn't want to deal with the grief he would receive from the Jews from being with the Gentiles. In Peter's defense though, for the entire history of the Jews, the message of God has been primarily for the Jews and now since Jesus death, the gentiles can be part of the kingdom of God as well. Now both Jew and Gentile are both asking the same question we ask every day, "What does it look like to be a Christian?" What do you think a Christian looks like?
The other issues here is grace verse the law. Do we still need the law because of grace? Here is a classic theological answer. Yes and No. No in the fact that the law does not save us. We are saved by grace and grace alone. We do need the law though to convict us of our sin and point us to living a more Godly life.
I love verse 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." Again the question is who do you live for? Think about it.