Well, first of all congrats on the impending arrival.
Just when you think life is laid out, nature throws a curve ball, eh.
As for the MINI, how far along the finance are you? Was it a car loan secured on the car? If you have paid more than 50% of the total amount due on the agreement you should be entitled to simply hand the car back to the finance company. So any negative equity on the car is the finance companies problem, not yours. Check your finance documents for the specifics.
Nae idea what your car would be worth, I'm afraid. Hopefully others will be along soon to advise on that.
A.