she canters in pasture and is a thoroughbred paint cross
Maybe you should check with your vet if she doesn't have a back or feet problem. Is she cantering in the field?
Then, what is her breed? Trotter? If yes, she is not used to that speed.
I agree with both @ellenmolin
It seems like you may need to do some groundwork so she will listen to you. After that I would just try free lunging her. It is much easier for her to canter freely rather than focusing on a circle. Every time she canters say “canter” so she learns voice commands. Then bring her on the lunge and make the circle big! It is much easier for them to go on a big circle. Then have her go to canter with the help of the voice command so she better understands you. Hope this helps and good luck!!
Initially, I thought this was a balance or strength issue until you mentioned that your horse tosses her head. Horses toss their head to communicate a protest to what you're requesting. For example, in a herd you often see proud geldings or stallions trotting around tossing their heads if they are trying to move another horse's feet or if another horse is trying to move their feet (act of dominance). It's not 'naughty' behavior (no horse intends to be naughty) but it certainly is not submissive or obedient and shows a lack of respect on your behalf.
You need to prove yourself to your horse that you can be trusted enough that she is willing to move as fast as you need her to. Consistent groundwork is essential. Simply making your horse run in endless circles does not communicate respect or confidence. You need to ensure she moves her feet quickly, with effort and you are asking with authority rather than nagging with the whip which so many people do! Move her feet back, left, right and forwards. Exercises such as yielding the hindquarters/forequarters, backing up, lunging for RESPECT (changing directions consistently) works brilliantly.
I highly recommend you watch some of Clinton Anderson's groundwork videos. They're very educational and if you put his ideas into practice then your mare will be much more willing to canter in no time. Believe me,
If you have access to a arena where you can free lunge, I would try there first since there’s more space. It sounds like she doesn’t quite have enough balance to canter.