QueenCheval - don't forget to come back and update us on this thread. I'm actively interested on how things go as like I said, we have all been through this before.
I had another lesson on Wednesday night, and it was with a new instructor. She asked me what level I was at, and I told her I could Goose get into a canter, but had trouble staying in it. At the far end of the arena, Goose and I did some circles cantering, but never got more than half a circle before she started trotting very fast again, which I think is messing me up. She asked for me and my riding partner to trade horses, because she had just cantered pretty easily, doing some hands-on-hip exercises on him. She put him (The horse's name is Rafferty) on the lunge, and I got him to canter pretty easily. Our instructor told me that I wasn't doing anything wrong, I just needed time to build stronger legs and a more balanced seat, which she said was hard when you only ride once a week.