Well head shaking like that is usually a sign of attitude, and not a good attitude. So, you gotta figure where that comes from. Is it just plain being lazy and not wanting to canter or is it that something about the canter feels bad, such as pain or discomfort. The horse is telling you something.
It can be just her being cantankerous. I guess you would have to see if she does this on the lunge line, when asked to canter. Does she do it if another person asks her to canter., Does she do it if you stay seated (not two point).
I think you should experiement a bit here to find out what is making this sour attitude. Of course , the first thing to ask yourself is if there is any pain issue, like an ill fitting saddle or some problem in her back or hips that is only really a problem in the unique movement pattern of the canter. Does she do this going both dirrections? on her own (unmounted?)