Do you half halt before you ask for a canter?
I agree that it looks like you need more outside rein and connection. Its so deceiving. The outside rein actually makes your turn. Ask your trainer if you can focus on outside connection for a few lessons because its very hard to explain and understand in text. You will need to feel it.
I like Tiny's mental image too.
I'm going to go against the grain here with regards to sitting to the outside. I think you are already sitting too much to the outside to compensate the feeling of her leaning on your inside leg. Completely natural reaction! But by doing this, you are actually encouraging her to lean even more to the inside. Think of someone on a motorcycle making a sharp turn - if the rider shifted his weight over the bike seat to the outside while pushing away it would eventually push the bike into the ground. When you are cantering, try to think of stretching your inside leg down more and think about the fact that wherever your weight goes, the horse is going to want to go under that weight to stay centered. That actually means weight in the inside stirrup. Not all of your weight, think about having 55% inside 45% outside.
Another thing, don't spin your wheels if the leaning becomes unmanageable during any stretch of canter. Go back down to a trot, re-balance and get your bearings, half halt and ask for the canter again. =)
Let us know how it goes!