I think there is another way to look at this also. Not just technically as in one room versus another but emotionally. When mom says to the child (I'm speaking in general here) "I can not trust you and you have no respect for me so it appears that we can't live together. However, I love you very much and I need to know that you are safe. So if you don't want to live here, then these are your choices: your dad's, another relative's, juvenille hall or foster care. What you may NOT choose to do is live on your own or on the streets. You pick and we will see what we can work out." In essence, to me anyway, the mom is saying I love you and I care about you and your well being, but we are both miserable and we need to make some changes.
This continues to support the child while putting your foot down about the child's behavior. In my opinion anyway.
I do hope this mother and daughter work things out. And now that it has been brought to the attention of the authorities, mom may be given more resources and this daughter, like many of us who posted here, will come around and learn she loves her mom and the rules aren't so bad after all.
Salem