RMM,
Sounds like you are in a very uncomfortable situation. Is he dating this woman? It just sounds yuck. If he wants to keep the house make sure you protect yourself. If he wants to keep it you have to get your name off the title and also off the loan at the bank which means he would actually have to refinance. My ex and I had a verbal agreement but only because I screwed up on the divorce papers and to change it would've taken alot of time and more money. He also knew I was good for my word. I had his name removed from the title so it was listed as my house BUT I couldn't refinance and was planning to sell so it wasn't so important. Because the loan was in both our names I had complete power to screw him over. If a payment is late, if I forclosed etc etc he was just as liable as I was and there wasn't anything he could do about it but make payments himself to save his credit. Just make sure you are not only off the title but off the loan. Very important.
I may be out of line here so please forgive me if I am but what kind of man uses his children as a bargaining tool for a house. Please make sure you cover your interests in this, it doesn't sound like he would be decent if it got ugly. Be careful!
Heidu