That student needs 100 miles of flat work before even hitting a simple cross rail. Why is she sitting hard and driving from the back seat? Amen to that overly tolerant horse, good boy.
I think she would've been taught to sit back and put her leg forward when she felt uncomfortable, there wasn't much wrong with the way she was riding and she was having a lesson to improve, not to have you knock her down because you think she isn't good. I found this video very educational.