The mother probably shouted to the child to get in the seat, so she could make a hasty retreat. The child, hoping to end the beating, did what she was promptly told. You may be right, but I'm sorry, I have not seen a hand strike the child in the video. I see lots of arm flailing by the Mom, but no contact.
Is it not possible the woman suspected surveilance and thought she could set up a false arrest sting?
I have seen mothers play with their children. I have seen mothers spank their children. I have seen mothers wrestle with their children. I have seen mothers trying to wave away an insect bothering their children. I have seen this from every angle; front, side, and behind. That mother was BEATING that child. I saw the video with the sound down, so I did not have to be told by a newscaster that the mother was beating the child.
Here's a question: if you saw the video, and it was of your babysitter doing the same thing in the video, with your child, what would be your first reaction?