"Fact": The man has a history if intimate partner violence, which makes the actual FACTS visible on CCTV that much more believable.
Please show your proof of this "FACT"

Question if the women's child came to her and complained that the other child was hurting her why did she not do anything about. 
You say (and there is no proof of this, in fact your the only person who has ever mentioned this) the girl snuck back in, there were 3 kids and 3 adults at the table and they were unable to keep track of the child?????????? I have 2 kids and often go out with them and I can always tell you were they are. 

The woman told the man to f..k off BEFORE he touched her child.

The man is a vile excuse of a human I have never stood up for him and never will, he lost any chance of defense from me the second he touched the other child. My argument is not about him being banned but about her NOT being banned. Her swearing and yelling and turning a blind eye to bulling are inexcusable.