The term in "quit claim." Quit claim doesn't change the mortgage. Your spouse's comments are correct, more than a threat. If she gets her debt discharged in bankruptcy, as soon as the stay is lifted, the bank can foreclose.
If your spouse quit claimed the property to you (it would have been better to have a special warranty deed), then you should be able to refinance (subject to your credit approval and the valuation of the property). I'm confused as to why the ownership of the house is in question.

