As others have said, you did the perfectly OK thing with a 6 year old. A younger child, you might have spoken to the parent instead.
However, with this parent, I doubt anything you did would have been right for her!
I am much more tolerant of ill behaviour in a 2-4 year old. I am still surprised how nasty folks on this board can get about a 3 year old for example kicking the seat. When our daughter was that age, her feet hit exactly the back of the seat in front of her. It was very difficult to make sure that she wasn't kicking - but you can bet we were vigilant, keeping our hands on her feet to stop her in the event that she started. However, at three, kids lack impulse control, so I think as long as the parent is clearly trying, there should be some tolerance.
But a six year old acting like this? And the parent clearly not trying? That is wrong.