The bottom line is you're not really in a position to make a lot of choices that involve money. I'm assuming you're a minor and still in the care of your parents. You've found a place where you can ride two horses a day, and at least get to call them "yours" even though that doesn't sound entirely accurate.I know the costs of owning a horse I've had one in the past but it had to be sold (outgrew and she was practically wild when we were told she was halter broke, with basic saddle training) after that my parents gave up on buying horses, and that's when I met my trainer. I would love for it to be as easy as "just moving on" but its so difficult because I met my heart horse at my trainers and If you met from horses in general, Horses are like my whole life, I love riding and training and even just hanging out with them.
You want to progress to doing more in lessons than your trainer is allowing, but a year of riding isn't that long. And it sounds like both of the horses that you ride aren't exactly reliable school horses that will pack you around at a nice canter (since you say you are the first one to have ridden either of them in years and that you're "training" one of them). You really need to learn how to ride on a well-schooled horse first and then you can take on the challenge of working with a less educated mount.
For now, I suggest you stay where you are and keep working hard and proving to your trainer that you are ready to canter. Let her know how determined you are...show her how determined you are. I remember being just like you when I was a kid taking lessons. I wanted to be like the other girls who were cantering and jumping and showing. I had cantered a few times in my lessons in the ring, and one day the barn owner allowed me to ride one of the school horses just for fun with the other girls...no lesson, no instructor there. I decided to canter out in the jump field and I may have even tried to go over a little cross-rail. The next thing I knew I was unable to stop the mare, had lost my balance and was nearly hanging off the side, and it wasn't until we reached the barn that she stopped and I slid off, my heart racing.
I learned my lesson. I wasn't as "ready" as I thought, and suddenly I knew why my trainer was forcing me to go slowly. She was an excellent trainer and eventually we cantered and jumped and I got my own horse (who was green and wild) and he and I learned a ton together and went on to be very successful in eventing. And through it all, I never stopped taking lessons. Even when I started teaching lessons, I was still taking lessons.
Sometimes you have to trust your trainer. Even when she's not letting you do what you want. There is most likely a reason...one that you may not realize yet. But definitely talk to her. Ask her what you need to be doing as a rider to prove that you're ready to canter. Then work on whatever she tells you. Work at it and show her how dedicated you are to being a great rider.