I think you have described a couple of different issues here. It might be most helpful for you to sort those things out:
1. Your house is upside down in value.
2. You aren't sure if you and your husband still own the property together.
3. Your ex is making all of this more difficult by confusing your children.
The last one has to be the worst. It's almost impossible to explain difficult things to children anyway, and this issue is doubly painful since you lived there as a family.
You have alot to sort out, but I would start by identifying what's really going on and deciding what things are worth fighting for and what battles you can't win. I wonder if your ex would EVER be willing to back off no matter HOW much evidence you give him to support your claim.
As for being upside down, unless you have a legitimate financial hardship, chances are the bank might not approve a short sale and/ or may hold you liable for any amount of money you're short, meaning the amount you owe the bank vs. how much the house would sell for. Make sense?
Good luck to you. I'd still consult an attorney, especially one who specializes in short sales!!!
If the modification was based on my income, they just want him still on in case I default, which I am not planning on. But with him telling the kids for the last two years I "took" the house, and it is his also, I am more than ready to move on! Plus, I feel the $70K in negative equity is a burden, he has taken me to court several times to try to reduce child support, I have court fees from that, I want to severe all the ties I can. If it means leaving the house to get rid of a joint liability, so be it. Since I will be getting more income soon, and I have great credit, any chance of getting rid of the mortgage in both our names? I can't refi, it is too far in the ground, I am assuming he can't either!
I don't know if there is an answer, honestly. Sometimes I feel a little jingle mail might be in order, but I do like my house, just hate the joint property ownership. I do tell the kids that the judge gave it to me so we could live there, and it is mine, but their dad tells them it is still his! Confusing for them.
Not sure what an HMA is. Do you mean HAMP? That means Home Affordable Modification Program. If so, then, yes, you have already refinanced. I'm a little confused about why his name is still on the mortgage if this modification was just using your financial information. Technically, the modification is just "modifying" the terms of your current loan which may explain why he's on there in name only and why they only needed your financial info to execute the modification.
You have a somewhat confusing situation with the divorce decree stating you get the property. Other than his name being on the mortgage, he doesn't seem to have much claim to the property at all. However, because his name is on the mortgage, if it went in to default and ultimate foreclosure, it would affect his credit and yours.
I would consult an attorney to see what your options are. Many times, attorneys will provide you with consultation time at little to no cost. Good luck and keep us posted on how this turns out for you.
This is a difficult situation that does not have a once-size-fits-all solution. I suggest meeting with a professional Realtor and a Real Estate attorney to go over options available. First meeting is a no cost consultation with the attorney.