It sounds like your mare is dropping her inside shoulder and being lazy. This is why it feels like she's cutting in on a circle. You want her to have a slight INSIDE bend so that she's rounding her circles, NOT an outside bend, as you've said.
Think of the reins as being extensions of her legs and feet. Your left rein controls the left leg, and the right rein controls the right leg.
So... whenever she drops her inside or RIGHT shoulder like this, take your RIGHT rein and bring it up sharply (not painfully, but firmly). The minute she drops her shoulder, IMMEDIATELY bring your right rein up, a sharp little tug. I find it helpful to say "lift up." It doesn't matter if you butcher your hand position. Bring the rein right up. You should be able to feel her lifting her shoulder. As you do this use your inside leg. Then you can resume hand position. The second she drops it again, lift up immediately.
You could also 'bite the boot' in this situation too. Hold a bit of weight in your outside rein, while shortening your inside rein and pulling her nose towards your boot. She should start to make small circles around you. Circle, circle, circle, until you're dizzy. Then go straight again. If she starts dropping her shoulder and doing an outside bend, IMMEDIATELY bring your right rein and say "lift up," using inside leg.
I hope this made sense. And good luck.