I have not every been married, so maybe I'm not qualified to answer. BUT

It seems like your husband may still be attached to the way his life was when he was married or living with his children. Not necessarily attached to his ex still, but his life.(?)
Has he been in counseling to deal with the changes in the life over the past 12 years? That might help him 'move on' or decide if he's even ready to or not.
I can't tell you if it's worth the trouble, because I don't know about the rest of your relationship. Only you know if this problem is overtaking the rest of your time with him. So you live together and you've only been together 1 year? How soon did you move in after you started dating? This could be stressing him out, or making him remember and cling to his married life before. Or not, I'm no expert.

Don't know if that helped at all, but let me just encourage you to stay strong!
*hugs*