I’m only 13 but I’ve seen many situations like this so I think I can help. I believe the reason why your mom keeps accepting this man is because even though he gets drunk and treats her awfully she doesn’t want to break up with this new guy because she’s so used to that type of relationship, I’m not sure she knows what it might feel like to have a wonderful real relationship where there is no abuse of any type and there’s just love.
Another part of it is she probably hates it when he gets drunk and abuses her. Infact she probably thinks about wanting to break up with him. Deep down she probably understands she needs to. But everytime he isn’t drunk and treats her nicely she loves him again which makes her feel like there’s hope even though she needs to let this guy go. I hope this helps, I’m so sorry you have to be in this situation though. I hope things start looking up for the both of you.