Well if the that is case, there is no reason to compromise with your mom. Being with your dad is the way better option for you (since he loves you and you love him) and maybe it is the best option for everybody involved.

Still I hope you understand that at some level what your dad did was morally wrong. Irrespective how crappy things were, the correct order would have been to seek divorce before hooking up/dating somebody else. Learn from the mistake he made.