Paul and Peter had a difference of a doctrinal matter (Galatians 2:11). The confrontation is recorder two times in scripture and both men go their separate ways.
Both men were trying to reach a target group in the community and both had adapted their approach for futher outreach. Still there was a confrontation that swept up even their staff and close followers, driving a wedge between their relationships.
I guess the bottom line is that they parted ways and their ministries were seperated at that point. Paul, reaching the Gentile-Christians and Peter reaching to the Jewish-Christians. Still they kept on serving God, just not with each other.
Perhaps the solution is just that simple.