Overnight at the Hospital

Calliope took the day off school. She wasn't sick, and I told her that she should go to school. She made the choice to stay home. There were several periods of argument, even yelling at her 3yo sister and breaking her toy. Things got really bad while I was trying to make dinner. She hit the 1yo, and I asked her to cool down in her room. She wouldn't, kept hitting baby Claire, so I picked up the baby, she shoved us into the wall ovens, hurt baby Claire's ankle on the oven handle. The bag of sugar in my hand was used to get her off of us. I got the little kids to get in the car in the garage. They got in their carseats, and Calliope followed us into the garage and kept hitting me. I closed the doors and backed into the driveway then finished the buckles on the little girls.
I called my sister to help me collect my thoughts then called local police to report the crime. They don't like hearing from me. There were no officers available to help us. Still two guys came whining about wasting their time on a kid that just needs discipline. I made it clear that I expected them to do their job; she is behaving criminally, treat her as a criminal. There is no way that threatening me with violence and murder daily is going be be okay. Hitting kids and beating up on mom while kids watch is NOT okay.
Anyhow I called the mental health crisis number and was put in touch with a gentleman that has been understanding and a help to us before. He took her to the mental health crisis hospital. She's still there. They're trying to figure out who is paying and how much before deciding what "care" is appropriate.