Asking for canter?

What you're considering is the correct way to ask for canter, maybe with an additional squeeze with your heels if the horse is lazy.

The instructors method will probably only work if the horse has been specifically trained that way. Pushing with your seat isn't usually as effective as it will just encourage the horse to run faster in trot and then maybe break into canter, which is not a very controlled way of doing it and will probably take a bit longer for the horse to pick up on :)

What you want to do is the correct way to canter. What your instructor is asking you to do is likely to just make the horse go into a faster trot and eventually run into canter, which isn't good. However she knows the horses so this is probably how they were schooled.

Just try your way and if it doesn't work, keep trying her way.

I ask for the canter by using my seat aids and I find that effective. Just keep on working on it and if you can, do a practice ride where you go in the ring with the horse and work on asking for the canter. Your idea will probably work but the best way to do it is the seat aids. It will take time to perfect the transition but keep working on it and be patient ;)

Make the strongest aid your outside leg behind the girth.

First sit the trot for a stride or two, and pick up the reins to let your horse know you're about to do something.

Slide your outside leg behind the girth a good 3 or 4 inches, and thump him, and give a smooch.