That girl’s mother is 100% wrong. Her behavior is childish and rude. I would absolutely get it on video because that is just the kind of person that I am. I don’t know what I would do with the video though. I’d be asking myself some questions, you’ve already witnessed that this family has a perspective issue and will make a mountain out of a mole hill.
What is the best possible outcome?
What is the worst that can happen to her?
Do you think her behavior is dangerous or is rude?
Is prosecuting her worth the backlash your daughters' are certainly going to get?
I would definitely speak to the family friends that are police and get their opinion.
I think I would treat her like the animal she’s acting like. Get an airhorn and every time she flips the kids off blow the horn. Of course that might irritate your neighbors...