Hi - it sounds like your girlfriend has serious mental health issues and the way she is treating her daughter amounts to abuse.

Mental health issues aren't a problem in themselves in a relationship, what it depends on is how mcuh the person is aware of their issues and how dedicated they are to resolving them.

If she is not dedicated to changing, is not in therapy, and does not realise her behaviour is wrong (i.e. she does it again...), then she will not change.

Answer to why you're in this: Because you're lonely. It's easy not to realise you're lonely, I never notice it either, I feel fine on my own, but if you are considering continuing a relationship with someone that abusive then I would strongly recommend you consider how you are feeling, whether you are lonely, and whether you could think about seeking help for yourself.