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If she will not sign the Quitclaim deed, you cannot remove her name from the title.
I'm not sure that a modification will really help you, as the result of most modifications is a modest decrease - usually around $100 - in the monthly payment, with up to 10 years added to the mortgage term. This means if you cannot pay the mortgage now, you will probably not be able to pay it after the modification.
And you will eventually have to deal with the second mortgage, which will also be able to foreclose once the balance of the first mortgage falls below the market value of the house.
Have you thought about filing a Chapter 13 Bankruptcy to strip the second mortgage?