J.G.
First make sure the kids never forget you are there for them. You don't want them thinking running away to god knows where is a viable option.
Don't trust the kids that she is paying his child support, they hate him they can and probably will lie about him.
Where are the kid's father?
Now the part you won't like, you have to sit back and be prepared to pick up the pieces. If he is a predator he will twist your words around to make her not trust you. Smile, whistle a happy tune and wait.
Sorry I can't be of more help.