If I was there and could tell if she was really hitting the girl, I would, at the very least, grab her and pull her off, and perhaps throw her to the ground.
OK, I just saw the video on Foxnews for the umpteenth time. Watch the first few seconds after she puts the girl into the car. She is CLEARLY, ABSOLUTELY pummeling nothing but her child. Once the child falls to the floor it is harder to tell, but one could guess she ain't swatting flies.
By the way, Fox has a great mugshot of the mother from a previous arrest.