You're going to have to do better than that. If he commits adultery an she exercises her right to leave as permitted by the Church, she should have the right to take her children with her.
Yes, if his adultery is provable, then she can exercise her rights as permitted by the Church, and carry out whatever is written out in the prenuptial agreement regarding spousal adultery (committed by the husband or wife), if it were to occur.
The problem with NOT having a prenup is a woman can "divorce" a man for no reason at all, and steal everything for which he's worked & built.