Quoting DaddyMike:" I have giving up on her. I told her tonight that im not playing her head games anymore and that if she ... [snip!] ... I am trying to get in to a law enforcement career and that I am going to school which i dont think will make me sound unfit."
Ouch, she's really making things difficult, eh? I think you are doing the best you can by moving on. Seriously --- someone who truly loves you would not treat you this way. Think about that if she ever tries to get back with you. This will never end well.
As for custody.... yes, she can breastfeed, but that's not a basis for keeping your child away from her. She can also pump. I would suggest you keep your nose clean, stay in school & do your best to look as stable as possible. Just because she is the mother, does not make her the best parent. Get yourself a good lawyer. And what ever you do --- DON'T argue with her, DON'T send nasty txt and/or voicemails and DON'T underestimate the levels people will sink to in a custody battle. Keep a log of everything if you can. Every interaction, every encounter with her. It might help you in the future.