I'm sorry because it sounds serious on her part. Selling a house can be stressful. I hope she realizes that any man she gets involved with will never love your kids the way you do. Women sometimes imagine that they'll find a great romance, and the guy will love the children, like they were his own. It can be hard to love someone else's kids. (I know that first hand.)
I don't know what advice to give beyond - get an attorney. You should each have your own lawyer. I'm sorry for the children. This situation is not sounding hopeful.