Her ex wants 51% because
a) He doesn't want to pay child support.
b) He wants the tax write off.
Bino, your GF needs to get her shit together. You can't do it for her. And she needs someone to advise her legally, beg, borrow or steal the money but she needs a barracuda to at least tell her what her rights are.
And as far as any court case fucking with the kids head. Little FYI, if the father is THIS much of a prick now, do you really think he isn't going to be badmouthing the mother to the kid up one side and down the other every chance he gets as soon as the kid is old enough to understand what he's saying? If you believe otherwise, I got an awesome bridge to sell you. That kid is fucked already. The less the father sees it the better.
My ex's favorite pass time during his every other weekend visitations was telling my son everything that could, in any way, be embarassing to me, including stuff that wasn't true. I'm talking shit a kid has no business hearing. Shit NOBODY would know except my spouse, or think (except someone like the truly bitter little bitch that my ex was). Let your mind dwell on all the things that could potentially encompass, considering I was married to this guy for 10 years.
Tell your GF to put on her big girl pants and go to war. That man will screw the kids head up just to get at her and feel vindicated in doing it. Freaks like that always do. He's willing to use the kid as a pawn and anything else he can as a weapon. She broke away from a manipulative control freak, they can't forget or forgive shit like that.