Hi, I'd like to help you with your questions.
This is a very difficult situation you are in. It sounds as if your daughter not only has issues of her own, but she is in an abusive relationship with the father of her child.
I would highly recommend suggesting to your daughter that she get counseling. She can contact the local community mental health center for a referral. It sounds like she may need to work out her issues with her abusive boyfriend and develop a more mature and emotionally stable way of coping with her problems. A counselor would be able to help her explore her issues and find ways to cope that result in better outcomes.
You could also attend counseling with her, as a family. The support would help and you could also work on her issues with her and the effects her behavior is having not only on her child, but your family as well.
If she doesn't want to attend counseling, maybe the pastor at your church can help with talking to her or offer a referral for services/support.
You also may want to consider talking with your daughter about getting custody of your grandchild. I'm not sure this is an option for you, but it may be the best way to help your grandchild until your daughter can repair her situation. Talk with legal counsel and see what your options are. If you decide to go this route, start documenting the behavior you are seeing, particularly with the child's father. If there are police reports that is helpful as well.
It is good that you are there for your daughter. Hopefully, she will gain a better understanding of her situation and be able to take on the of being an adult and a mother.
I hope this has helped you,