Find out what your lawyer has to say about the deal. I suggest moving the car to a new location, deregister it, and finance a temp car. This way she won't see it as an asset (what good is a broken car sitting in a relative's garage to her). Then once the divorce papers are signed, sell the car for cash $8000 would probably be a good price. Take the money and pay off the financed temp car. It's important that you hide money from her. If you look dirt poor your lawyer is going to have an easier time getting your clear of her debt in court. In fact you may be able to countersue for credit dammages after the fact.
For your sake I really hope you had an aggressive prenup with fidelity clause.
"The 300ZX Turbo is a dance; it's a song; it's rolling, roaring automotive art. There is no color that doesn't suit it. There is no mood-lifting chemical substance it can't replace." - Automobile Magazine