Agree with others about the hands. A little busy, but better to see someone following a little too much than have a death grip on the horse's mouth. Since you are only doing weekly lessons, I don't want to trump what your trainer is telling you. He is obviously doing a nice job with you since you ride that big canter very nicely.
A tidbit on rein length and movement proportionate to the horse's head: Longer reins with your elbows at your sides will result in far more forward/back hand movement than shorter reins with your hands about an inch higher and forward of the pommel. The latter requires supple elbows, but gives a much more consistent, spongy contact that most horses love. Rein length and contact is something that many riders struggle with, and you can't just play with that alone. It has to also involve the way you are riding the horse in terms of the impulsion and rhythm. Again, this is just info. I like what your instructor is doing with you. When the time comes, I am sure he will impart this knowledge on you.
Welcome to forum by the way!
You just have to see your distance...you don't have to like it.