Siblings DO fight sometimes, and my own boys have sometimes caused each other to bleed when pushing each other down----someone will get a scraped knee or something. I have to admit that I have never thought of this as "family violence" because in my mind that would be something much more serious than a shoving match. The girls don't seem to be injured, and my opinion is based on the assumption that any injuries were minor.
Either this fight escalated WAY beyond anything I've seen, or the area has a "zero tolerance" policy whereby they consider all fights between family members to be "family violence" or the police overreacted.
I get the point that we all want the momma to have the child take responsibility and not "baby" her into thinking she can knock people around, but I totally understand the mom's frustration over her daughters fight being forced into the legal system rather than being handled by the parents in their own home. None of us really know whether the mom would have handled the situation properly or not.
Sometimes I think we've gone way too far in one direction in USA. When we arrest five year olds for having a fork at school and 10 year olds for fighting with their sisters, I wonder WHAT we'll do for a TRUE instance of violence. I may have shared this with y'all before, I can't remember. I had a son in the 6th grade who was on recess break at his middle school---their recess area was barren of trees, no benches, no climb toys, no balls and bats, no nothing. My son and his best friend found a bottle top on the ground and began tossing it back and forth to each other, and the principal called me to tell me this was VERY serious. She could have had both 11 year olds arrested for assaulting each other, but out of the goodness of her heart, she was only going to suspend them each for 10 days. That's the day I started reading stories like this one with quite a different eye.