Sounds like she would like to keep this “marriage in name only” for convenience’ sake.
It would be better for the boys to stay with him and for her to go. Girls would be the opposite situation. He could offer to pay her a lump sum to just go, then he would have no more need to fume. Let the new guy have the trash on a silver platter.
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)