Why would it be better for a girl to go away with the cheating mom, and live around that kind of man? Daughter would be just as good to be with dad. In fact, a good argument can be made that a daughter needs a solid dad even more, or at least as much, as a mom. (especially a mom with a problem like that)
I’m guessing a daughter would probably be emotionally torn less that way, especially if there was visitation and the pair tried to make their parting as externally amicable as possible. But since there are only sons, they would definitely do better with dad and just dad. They would hate this new guy’s guts if forced to be with him.