Kinda of depressing but need some advice.

Try to imagine if you will regret it more if she is there or if she isn't there. Focusing on your mental health and your wedding experience is the right way to go here. Trust yourself and you will make the right decision.

I think it would help if you relinquish the idea that you are your Mom's caretaker. She should not get sober by your wedding deadline. Her recovery is her own to handle.

Invitations go out 6-8 weeks before. Ask yourself if you think you'll be worrying about birth Mom throughout your wedding day. If it's still yes by the end of the summer, then eliminate stressors and inform birth Mom you prefer her to not be in attendance. Say imposing your ideas of sobriety are inappropriate for her personal recovery, and you want to focus on yourself and your FI that day.

Im a few months late to your post but i feel for you so badly. My mother is an alcoholic. If she drinks she makes a complete fool of herself and her family. If she can't clean up her act and behaviors or take accountability for herself i see no reason not to invite her. The day is about you and your happiness. It does not seem like your mom has ever tried to make herself better for your sake or happiness so why should you take her feelings into consideration if she is stepping all over your feelings? I am also considering not inviting my mother as well.

I hope you have a beautiful wedding and wish you all the best.