It sounds like you need legal advice, so see if you can get a lawyer to help you limit your financial liabilities during your legal separation with your pending divorce. It sounds like the only problem you have is the car payment on her car that is in both of your names. But since you both signed the contract there seems to be a joint obligation and responsibility. Again — I’m not a lawyer, so you should seek appropriate advice. Ultimately, this and other financial issues will be settled when your divorce is finalized, so don’t dawdle on that issue. Limit your liability.
As for moving out of her mother’s house, you should find a friend to move in with or a relative who will put you up until you can get your divorce finalized at which time your financial settlement will be clear. Doing this will limit your heartbreak as your soon to be ex-wife starts testing the dating waters under the same roof.
I hope that helps.
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