Ginger's biggest problem about the lead is that she just doesn't really have the muscle/strength for that side yet, so it's uncomfortable for her.
Agree with you and your instructor there! Barring an injury or something, that's almost always what it is. They're right or left-handed just like us, and their muscle-memory makes one lead more comfortable/familiar than the other, especially when they're not at top fitness.
I'm sure your instructor knows more than me, plus she has Ginger right in front of her and can tell what to do for her, but here's a couple things that have helped me when a horse has a hard time picking up the correct lead on their weak side:
1. Say you're going around in a circle to the right, you ask for the canter, and she is obedient, except she picks up her left lead.
Instead of bringing her back to the trot and asking her again, just praise her for cantering and let her keep cantering on the wrong lead, but gradually make the circle smaller until it becomes more comfortable for her to change leads, than it is to continue on the wrong lead (make sure when you do this, to keep your own weight completely centered, so that it's her own balance that makes her want to change leads.) When she changes, praise her A LOT, keep sending her forward, and gradually make the circle bigger again, until she can canter a few circles in the correct lead. The first few times, she might break to the trot or go into a cross-canter (front legs on one lead, rears on the other) but this is only because it feels awkward for her. Keep repeating the exercise, as long as she's not tired.
This way, she doesn't become frustrated, thinking, "you asked me to canter and I'm cantering, but you're acting like I'm doing something wrong, I don't get it!" Because "going forward" is always the right answer, even though going forward on the wrong lead is not the perfect answer, you want to reward her for trying.
2. Once she is capable of cantering circles on the correct lead, even though you might still have to get it by starting off on the wrong lead and shrinking the circle, she's developed some muscle-memory of cantering on the correct lead and it won't feel as awkward to her.
Now you can start working on getting the right lead in the trot-to-canter transition. This takes some perfect timing - ask for the right-lead canter when she's heading for the corner of the arena (kind of faking the "smaller circle" exercise) and ask for it when you would normally be sitting your post (I have to keep counting "up-down" to myself, even though I've actually quit posting a stride or two earlier to ask for the half-halt) so that her rear outside foot will be the one to push off into the canter.
Sorry this ended up so long, but hope it helps a bit. Ginger is a lovely horse, and you're making amazing progress with her.