It's your baby as well, it is your business regardless of the situation. Put your foot down and tell her that you're the kids father, you have EVERY right to go to appointments and see how YOUR child is doing.
Tell her that if you cant see how your baby is doing, then you're not gonna buy baby stuff for her. Buy baby stuff for yourself and that baby. Screw your ex. Just take care of the BABY and YOURSELF.
