I've never been a mentor, but she seems to be avoiding you for some reason. Is it possible to sit her down and have a talk about what she's feeling or going through right now? Being a teen parent is tough no doubt. She can't do anything she used to and she's probably really upset about her mother in more ways than one. She has to face alot of shame that society places on young mothers as well as un avoidable shame in what her mom is going through.
Let her know that you're really interested in being there for her. She may not have had anyone really show her that they care so therefore she may not be used to such treatment. Try your best not to give up on her, but at the same time , don't lay down to play doormat either.
I talk with all the young girls in my neighborhood and I listen without judgement then offer as much advice as I can. So many were just happy to have someone to listen to them, and others thought I was in it for some sort of gain. I'm not a "mentor" so to speak , but I've talked with many young girls. They need more people to take interest in them (Mainly parents) and I applaud you and your efforts!