If you have some chocolate, eat a piece before reading this, because you're going to hate the idea and get a sour taste just reading it.
No, seriously. Eat chocolate before reading the rest.
Okay, now take a deep breath.
Ready? You're going to hate this but read the whole idea and consider it before dismissing it.
Your mom isn't a pleasant person, but she's good enough to take care of your daughter? Can you hack living with her for two years? And, if you can, would she let you move in?
Because you have a mom, she has your daughter, and your daughter is 16, so she's leaving in two years one way or another. (Kids are itching to get out of tough homes ASAP, so she will leave then.) I know it may not give you any more peace to move in with your mom, but you need a place to stay until you can get the degree, and she's not your husband, so you won't have to live with what you have now. And, obviously, you don't get along with your mom, but can you survive her? This seems like a possible way of repairing the relationship with your daughter a bit and keep you both sheltered. And "only two years."
In two years, you'll be done college and your daughter will be, at least, ready to go out on her own, so you'll be more settled in to your own life with a better possibility of giving your daughter a better place to live if the thing keeping her off the handle is the family relationship. (Also, be aware she is 16, so she won't be easy to reach at this stage, but better time trying with her than not being able to try at all because you're struggling.) Sometimes we can only start for lasting relationships, and if you wait until you are settled, your daughter is already on her own.
This seems like it won't be much better, but at least it gives you the time and, maybe, the safety you need until you are ready.
Sometimes we're left with "This sucks, this is suckier, and this is the suckiest." You're already in suckiest. Which sucks less -- living with your mom AND daughter or struggling on your own by starting over from scratch?
(And eat more chocolate after thinking that one over to calm down and remember sometimes life is good enough to give us chocolate.)