I agree he didn't necessarily seem abusive. It seems she was giving it right back to him. Perhaps, that's how they relate to each other.
He was, however, one of those annoying parents that won't shut it during a the lesson. He should let the coach do his job.
As for her game, it does look loads better in the videos you posted. In the first video, her balls were all over the place. I wonder what the coach was trying to accomplish. It looked like a mess though her racquet head speed was tremendous for her age.