I have run into people where they have a divorce and need to short sell the property, However a quit claim deed has been signed and the damaged party has no rights to the property. Good luck and I hope everything works out.
Is his name also on the mortgage or is it just yours? If it is ONLY your name on the mortgage, all I can say is "How did that happen?" because that is NOT a good thing.Being behind on the mortgage for the past two years is impacting your credit report and scores. That is hurting you and you don't even have control of it.
As far as "what rights do you have" if it goes to a foreclosure, really none. Once it goes to the Sheriff Sale, you have a 6 month redemption to reclaim your home, and pay all the back owing payments in order to do so. The banks can come after you for the deficiency if they choose to, after all you are the primary. Why does he care if he's paying late, you're the one being hurt. Did you have legal representation for this divorce? I can't believe a lawyer would not address that issue.
It's too late now, but see if you can get the ex to refinance the home JUST under his name. If there is equity in the home, he may have a chance even with all the late payments, but most likely it sounds like he may not be able too. The bottom line is, do what you can to get your name off of the mortgage.
If you can't, then go speak with a lawyer about what you can do in case the home eventually goes to foreclosure. It is better to be prepared, than surprised and unprepared when it happens.
I hope this helps a bit,