I remember your thread aways back about the head tosssing and showing both you and your trainer riding. With that in mind, I see huge improvement. You should post those older videos here, too so we can see how much ground youi've gained.
Your mare is so darned cute. She looks really good there. You are getting much better at creating some good contact with her. Trouble is, you still don't keep it steady enough so that she can find it and keep it. She does worry about her mouth, and that is a sure sign that you don't have a steady enough contact. What the above person said about your elbows and arms and hands will help a lot inmaking the contact soft but steady.
As you go around, I see some "flapping" in the outside rein. If you could really focus on having THAT rein be really steady, all the time. Try to do you following of her mouth with a mental focus on the outside rein never getting loose enough to flap with her trot rythm. To do that, you will have to use an active inside rein to get some bend, and when she does, give her a bigger release than usual. Exaggerate a bit, so that for a few steps she is on ONE rein ; the outside. IF she can hold that bend that would be awesom . And since she is touchy aobut rein contact, having her earn a big release on the inside rein will please her and let her know that she can earn freedom there.
So, get the bend, give a big release, like a looping rein, and then praise her or reach forward with your left hand and stroke her neck but keep the outside!
As for your seat, your postition isn't bad. YOu still don't have enough weight down and through the stirrup and this was noticaeable when you transitioned to a walk; you tipped forward. As you went around I saw that the stirrup was too far forward on your foot and seemed not weighted enough. Open your legs off the saddle (straigt off , like doing the splits) , let them drop down to the saddle, lift your toes and find your stirrup. AS you trot, think about mentally anchoring your heels toward your horse's rear feet. Elbows back, hands on top and engage the core.
Sometimes it looks like when you ask for more engagement from her that she rushes a bit. Her natural rythm is quick and short and you should't try too hard to change that. But, in order to get more engagement you do have to put leg on. When you do, if she interprets that as "go faster", you have to sit a bit heavier and breathe out and keep YOUR posting rythm unchanged, so she may rush one or two steps, but she will slow down to match your body and the idea is that the increased energy will become more of a reach under her body and lift of the back, rather than a fall forward and rush.
I see very definite improvement! Really good.