She very clearly has a tendency to pull and bare down on the reins by curling herself in and driving onto the forehand. She appears to be relying on your instructor to hold her up.
Riding her with her poll up and slightly in front of the vertical, not allowing her to come lower and bare down will help to get her thinking 'up' rather than down and out. What she is doing here is not 'long and low' or wanting to stretch - she is pulling the reins out of the rider's hands and trying to pull down to evade.
My little WB gelding does exactly the same and it took me a good couple of months to consistently get him to stay up and think up rather than bare down.
These sort of horses you have to ride very tactfully, and think every step. You can't stop mid stride to celebrate when you get a couple of nice steps - you have to keep riding every step and be skilled and sensitive enough to feeling when she is about to bare down.
Use your legs to bring her up - by not allowing her to go all the way down, you have much more control. So the second you feel that she's wanting to dive, put your leg on and pick her up again.
In the downward transitions, this tendency to nose dive is going to be your worst enemy. I would bring her up even high, poll as the highest point and above the vertical, prepare your downward using half halts to rebalance her and encourage the hind quarters to step through, then ask for the transition with your seat only, and allow your reins. If you start making a grab for the reins to make the downward, you will enhance the diving problem.
Good luck with her, she's a nice little mare and I really think you'll be able to make something of her once she comes out of this evasion.