That so-called "mother" should have stopped her daughter as soon as she started acting out. If you don't discipline your kids, someone else will, and you might not like how they do it.
I acted up when I was in a hardware store, and my dad gave me a time-out by having me stand in a corner. My acting up was nowhere near as bad as this, and I never got a time-out in a public place again.
If Bobby Knight was there when this happened, he might have picked that little girl up and thrown her into the nearest wall or out the nearest window.