I thought it might be a pain issue. I check her back before and after every ride and there's never been a problem. Her saddle isn't a 100% perfect fit but it's not to narrow and doesn't rub her withers. And she doesn't show any signs of pain when she's ridden by herself.
I also thought it might be something that happened to her in her racing days. Maybe she learned to associate the sting of the whip with a horse approaching from the rear. I have no idea.
So far she's only kicked at one horse (she missed). But she always pins her ears and slows down. I don't know what to do other than to keep her moving forward when she slows down so the other horse doesn't get within kicking range. How can I correct this? I ride in group lessons all the time and plan on showing her this summer. If she keeps this up she may not miss the next time she kicks.