Actually, I'm not so sure I agree with what seems to be the "accepted take" on this situation.
It's very possible that Mom and kid are at the end of their rope in this. Girls bully just as much or more than boys do. It's quite possible that after being "called out" by this Espie girl, with her friends egging her on, again and again, making the daughter's life miserable.
Mom, getting fed up, finally told her daughter to stand up for herself, and went down to the park with her, cheering her on.
I know this is possible because I watched the video and can see that this isn't Espie's (the other girl) first fight, and she's creaming the daughter.
I know this is possible because my Mom did this precise thing for me-- and it put an instant stop to a long string of bullying incidents. (Oh, and that kid creamed me too.)
Fortunately for me, and for her, she did it before the armchair quarterbacks and amateur psychologists took over and installed a victim environment-- and before the internet and instant viral videoing.
I am with you. My son was constantly provoked by another boy (that he used to be friends with) for the better part of their first three years of High School. It all culminated with 3 truck loads of "cheer leaders" and the main antagonist showing up at my house one afternoon looking to make good on a threat he had made to my son earlier in the day. My wife called me at work (about an hour drive from the house) to tell me what was going on. I told her to call the police and that I wanted to talk to my son. I told him that it would be OK if he just went in the house and ignored them, but that I understood his “need” to do what had to be done. Long story short, he tooled the kid out real good (much to the chagrin of the video phone taking idiots for a later post on YouTube). I was very proud of him, by my pride aside, he got this kid out of his face once and for all, and believe it or not, a more than mutual respect was restored.