At least you still have the baby, right? (If you're not laughing, Google "baby" and "bath water.") Financing a major purchase for a "girlfriend" could end up disastrous for you. You need to form a child-rearing corporation with her first.

buying a new car is for chumps. buy a used car you know will last a few years before needing any major work. I bought a mustang with 98000 kilometers and the first time I took it in for an oil change they said the engine was cleaner than most cars they get in. 3 previous owners, but each one took care of it and after 3.5 years of ownership I am starting to come up on needing some work on it. cost me the same as a new standard Toyota for a great condition car I have wanted since I was a kid.

If it's so embarrassing then she could always buy it herself.

All of the wealthy people I know buy used cars, because you don't get wealthy by needlessly going into debt on rapidly depreciating assets.