“ is she entitled to the mortgage interest paid on the house while we were married during 2010?”---> Yes, she is as long she( and her name in on the loan) actually paid the mortgage during the year. I am not sure if this is your situation; however(if it is), some common problem many people face in a divorce is; a court order directing division of the equity of the home in no way affects an outstanding mortgage. To change the mortgage, there needs to be an assumption, a re-finance, or a sale. There is no other solution. You can ask if the bank will take your ex-spouse’s name off, but they have no incentive to do so. The other option is to leave ex-spouse’s name on it if she doesn't object. Her ownership interest is gone since she gave you the quitclaim, so that's not a concern. If neither of these options will work, you have to refinance.What I mean is that you can’t get your ex-wife’s name off the mortgage without her having to refinance or a sale. A mortgage is an agreement between you and the bank. The only way to get your ex-wife’s name off the mortgage is to sell the property, have the mortgage refinanced, or have her assume the loan. If she were ordered to assume the mortgage, it was her responsibility to take care of this. Should she fails to make mortgage payments and if the bank should come after you, then your recourse would be to take her back to court to compensate you for what you were forced to pay the mortgage company.
Also, as your divorce decree was final on 12/16/10, you are NOT married for 2010 at all; you can file your return as either HOH or single, not MFJ/MFS.