It sounds like she may be picking up momentum to keep her balance to the right. Does she fall in on her right shoulder? Which way is her head wanting to go? If she is falling in and wanting to pull her head to the outside, then come back to walk work and focus on putting more weight in your right stirrup, you want to block the barrel from shifting to that side, use light right rein until you feel her release to that side. Make sure you are not dropping your weight onto your left seat bone to push with your leg, try to keep balanced and work on weight shift. Do this at the walk for a while and your canter will improve. When I say a while, I'm usually talking about weeks + to change the holding pattern, but make sure that you aren't moving everything too much to the other side, be very aware when she starts holding the change on her own.
If she is very down hill and almost falling with her head to the inside, work on keeping weight in the left stirrup, but place the seat bone further back in the saddle, like you are trying to push her barrel forward and to the right.
Balance is very tricky with horses, and something a lot of people take forgranted. The faster you go, the more balance is compromised. A simple weight shift/seat change in the rider can do wonders for how the horses weight is distributed. Without seeing the mare travel, its kind of hard to figure out why exactly she is having trouble going to the right and exactly where the weakness is. I gave you two very opposite solutions that would vary depending on where the issue actually lies.