That's quite an ex to have to deal with. My only advice is not to let her craziness and lack of moral character interfere with your marriage. Your current marriage is the #1 relationship in your life. It has to be put above ALL other relationships. Your ex should be way down at the bottom of the list of your priorities. In fact, the only thing you should give a crap about concerning her is that she's the mother of your children. Considering her horrific parenting, however, I'd already be contacting an attorney that specialize in family law and go for 100% custody. You seem level headed and responsible. With your ex those kids don't stand a chance. The boy will end up in jail and the girl will end up pregnant by 15.
