RPGs are storytelling games. Tell a good story, and everything usually works out.
Good stories where characters come into conflict require resolution. Either they kill each other, or they work out their differences and come together to beat a common foe. Whenever I have PCs and players in conflict, I give them something in the story where their combined efforts play off each other and result in a big win for the team.
To think of it another way, there is a saying in the NFL that only losing teams have bad locker rooms. Winning fixes a lot of problems. If things get too angsty, give the group a flashy win and a lot of problems dissipate.