I did have this problem back a few years ago now when I first got my super bouncy and elevated TB. His trot and canter were well beyond that of my old cob's and it was almost like learning to ride all over again.
Firstly I'd practice a lot of sitting trot. This will hopefully get you to balance and drop your leg lower and open your hips/pelvis. This should then lead on to a smoother canter transition and not through you off balance so much to begin with.
When I was having troubles, my instructor at the time was telling me I was leaning forwards and up out of the saddle in a very much forward seat. I could have argued the fact until I was blue in the face as I was sure I wasn't! We ended up practicing canter and her telling me to 'sit up straight' constantly until I seriously felt like I was leaning back. All of a sudden it all fell into place. My bum didn't leave the saddle, I got the movement and followed it, I was sat 'underneath' myself (almost like tucking my bum in...
) and felt like I was really riding!
I guess what I'm saying is that you may feel like you are doing right and it's not working. When in reality, you may be leaning forwards, tipping or unbalancing yourself before you even start. Really try sitting up straight, so much so that you feel like you may be leaning backwards (in fact, that may just be me that feels like that... not sure
).
Have you got an instructor? From your post it sounds like she's either not very helpful or you haven't got one? Either way, maybe look into getting another/new one and really put over your concerns and what you want to work on. Explain you have confidence issues as well. Maybe a lunge lesson would benifit you as well? You can practice the riding bit without the controlling the horse bit
.