You dont say how long you have been learning or what you have done so far. But what you describe is a very common problem.
Most riding schools teach students to sit the trot and then to ask for canter.
To make it harder still they ask students to do the sitting trot and ask for canter at the corner so the horse strikes off on the correct lead.
It is harder to balance at a corner.
That is why some teachers like my own teacher teach stiudents walk to canter instead.
Sitting well balance in trot at the corner take practice but ou will do it in the end.
But to get the canter you dont need to kick. Most of us dont kick horses ever!.
The secret of asking a horse to do anything is to prepare first, so the horse is able to do what you ask.
Before I sit to the trot, I make sure the horse is trotting really actively. If you do this extra active trot, with nice contact in the reins, coming up the long side and aproaching the corner of the school, most RS horses will expect to be asked to canter at the corner.
All you need to do then is to relax your hands, touch your legs gently and briefly to the sides of the horse, and allow the horse to move freely forward between your thighs and hands. I often say the word canter too.
The allowing is important.
You have to want to canter - and this is a contradiction as the first time you are not dsure what is going to happen. It is best to learn to canter in a lunge lesson. Then te RI asks the horse to canter and you can learn to sit canter smoothly without worrying about brakes and steering.