As I've said, I know some will disagree, but it's still my opinion to not turn her in. Do you really think the police will make matters better? That if she gets a record and a negative experience from the police that she will stop? Most people's crimes only escalate after an arrest. I think what she needs is some help in the form of therapy. I know she may not go willingly, but you could give her an ultimatum of either turning her in or finding another place to live if she doesn't (if your mom will go along with that).
In my original post I said I would never turn a member of my family in unless there was a case of abuse. Clearly the mother here is being physically harmed, but that was not the original concern outlined in the OP, it was the ring. Turning her in for abusing her mother is a different story, and IMO, up to the mother to do (she is an adult, not a child, in which case I would suggest anyone report it).