My son is going out of state with his job and has his daughter right now. The mother left the child in my son's custody because she's running from the law. If she comes back, can she give temporary custody to her brother, or can my son give custody to myself or his sister?

Your son needs to get his custody protected by the court. If she is hiding from the law, getting his custody established should be fairly easy. She would then need to get her custody/visitation restored through the court.