If you do this and she is a rational human being she will slowly start to meet your needs too.
Just want to point out - she may not be a rational human being (your GF).
And drinking before going to a child's game because she's "anxious"? Sounds like alcoholic behavior to me and very worrisome.
Also - get a second car seat. You shouldn't be home with your baby without a way to transport them to medical attention should the need arise.
I know everyone has been all over you for the mistakes you made in the past - not helpful now that you're where you are. Focusing on yourself is still the best thing you can do at present - not arguing and trying to be "right", speaking her love languages to her without expecting a tit for tat, etc. It may sill not work out because she may be an immature self-centered person who isn't capable of growing up, but if she is, this is your best chance.