My friend has had a fairly bad relationship with his dad (and girlfriend) and his answer was moving out. I mean, I still don't know about that. I sometimes think we young people can be fairly selfish sometimes and take actions without a clear head.
If the fighting is a normal occurrence, then maybe that just means they need to try and fix it, if possible. Talk, make amends. Really, I think if there isn't a violence situation at home, she should probably be with her family. But again, I do not know the issue.
If she honestly can't stand the idea of going home, then it is good for her to know she has a way out. However, I think it would be best to like, try and discuss through the problems she's having at home... her telling her side, and you or another friend trying to see the point of her grandmother and family. If she honestly believes her grandmother is selfish, I'm doubting the grandmother explains why she does what she does. We sometimes only see our side, and it sometimes help to hear possible explanations.