Hi, thanks for your question. You should hire a lawyer for specific legal advice. No attorney client relationship is created here.
This is more of a divorce matter than a bankruptcy matter.
As for the bankruptcy, a debtor can list any liability on a debt, and discharge it though the bankruptcy case. She can surrender the home and let the bank foreclose. Mortgage debts, utilities etc are all dischargeable in the bankruptcy case, including any verbal contract
with you for her to pay 1/2 of the expenses.
You can surrender them too, and they will discharge for you as well.
Absent that, if you want her to pay, you'll have to negotiate that in the divorce settlement agreement, otherwise the bankruptcy would discharge those obligations.
It may be best to just surrender the home, forget about trying to short sell in this market. let the bank foreclose, and any deficiency is the bank's problem after you each file the bankruptcy case.
Let me know if you have any questions. thanks in advance.