I am a RS rider.
I will advise you with what my RI would say. When you want a horse to do something, get it in the position where it is physically able to do what you want, then ask and free the horse to carry our your request.
Preparing to canter, remember that a horse can canter from walk or even from halt. But it cant canter from a fast spread out trot. To push off into canter it needs its hind legs under its body. If you are in a fast trot, the legs are unlikely to be under it for canter.
So as you approach the RS corner where you want to canter, it is a good idea to use leg to get a more active trot, (may be in the second half of the long side) but shorten the reins and sit up so the steps are shorter and the leg is under, ready to canter.
I never mastered the RS Canter aid. Yes you need to give a kick, but you also need to relax your hands and picture the horse flowing forward into canter between your thighs. And between your hands. If the first steps of canter are too violent, steady the canter by closing your shoulder blades together a little or sitting up.
The second question is also important. How happy are you in canter? RS horses sense if a rider is scared. I love canter because I learned to do it our hacking. RS horses know I like canter and do it easy for me when they refuse for other students. Breathing and relaxing is a good idea. Think of flowing and allowing the horse to move forward under you, rather than asking and yet inadvertently holding the horse back. If you would be happier hanging on, think of using a neck strap or monkey strap so you dont hold onto the reins. But actually I like to hold the reins. I need to feel in control. Just remember though, to hold the reins is not the same as hanging onto them. Your hands are allowing the horse to go. And the going is likely to involve speed. If you are an adult and a car driver, think of acceleration. and dont let the outside rein go loose. The outside rein will keeo the canter to the outside of the school.
I woud also in advance make up my mind that I am going to canter down the long side and trot at the corner. It is good for both the horse and you to have some sense of intended destination. You can even trot the short side and canter again at the next corner.
As for sitting the fast trot. One prepares for that by sitting trot and trotting without stirrups (properly supervised in a lesson) but in the ed yes, the trot before canter is bumpy for a ew rider which is why you need to keep it quite short. Dont hesitate, just a few steps and get into canter a.s.p.