I watched all of it. I think you are doing Clinton Anderson style stuff, right? I don't know a ton of his stuff but I recognized some of it.
Overall, you are doing quite well and have made some amazing progress with the mare.
Some things I noticed:
I am not sure about the scratching the horse on the face with the whip. Is that supposed to be her reward for backing up like you asked her to? It doesn't seemlike something a horse would consider a release of pressure, but rather something it must tolerate. So, that has me a bit confused.
The other thing I find confusing about CA is when you disengage the hind quarters, but the lead rope is so short that the front end is being pulled around almost on top of you. It looks like the horse is moving into you, or following you .
And that is a ton of backing in one session
Those are things I am not used to using.
I think you do well. If you want some suggestions, well, what I can say is that sometimes it seemed as if you "pressure' (whether that was the stick or your waving hand) came on somewhat suddenly , went straight to a middle level of pressure and stayed there. What I mean, is that I couldn't see the starting cue which would be very soft, an increase in pressure if needed, and an easing of the pressure when the hrose is indeed backing up. It looked rather constant in level of intensity.
If you want to build lightness in a horse, you must always start with the lightest cue, and build up to what it takes to make the hrose make a change. The build up (I mean the rate at which you increase from 0 to !) can be fast or slow. If the horse doesn't understand, then I think it should be slow. If the hrose is blowing you off, then you get firm more quickly. But you do offer them the chance them the good deal first.
Also, you won't always have the stick with you, so being able to cue the hrose with your body or hand will be your goal, won't it?
Also, I think it might be nice to give the mare some time to just soak on things, where you stand with your core pointed away from her and let her just be. not scratching with a whip or such.
Again, during the lunging, you brought the "go" whip up and around and down wthout offering her the chance to "go!" with a lighter signal. It's important to prepare a horse for a change of direction. If it's done without preperation, it's very irritating to the horse. One way you can prepare a hrose for a change of direciton is when you disenage them, rock them back on their haunches a bit, then point, lean your body , kind of take in a breath, raising your energy and see if you can kind of "roll them over" into the new direction.