Honestly I think particularly at the lower levels the canter transition is more about the horse’s balance and willingness to go forward than precision of timing of aids.
I get why the suggestion is to put the leg on at the right moment in the trot footfall pattern, but if the horse is not balanced and forward they will not be able to respond promptly even if the cue is perfectly timed.
Conversely, if the horse is balanced and forward, you can get a good transition just with a voice cue. I know that won’t work for a dressage test but I point this out to show that the horse needs to be physically and mentally ready to canter.
Here are some of the things I’ve seen go wrong.
Not letting go of the horse’s face, trying to keep a green horse in “frame” either from rider fear or desire for a headset.
Horse not being balanced enough and on the forehand so they fall into the canter rather than lift into it.
Horse not yet physically comfortable with cantering in the confines of an arena or on 20 metre circles.
Horse allowed to get generally behind the leg and under tempo, often because rider is more comfortable that way, so the energy for a prompt transition isn’t there.
Or there is something actively bothering the horse, hocks or saddle fit or something. I assume she can canter nicely at liberty or on the longe line.
As far as mare being unhappy about outside leg aid, is she unhappy when you use the single leg for lateral work? If not then what she is telling you is not “I hate the leg aid” but rather “I know you are asking for canter and I don’t want to.”
If you change her physical relationship to canter (balance) and mental relationship (energy level) so she wants to canter then you can work on timing of aids.
I made some mistakes in this regard in the early days with my mare, pushed her to canter before she was balanced, and she has never let me forget it.