Sounds like something could be physically wrong, if she’s never done this before. Check her tack- saddle, bit, bridle, everything, make sure it’s fitting properly. If it is, or if you’re not entirely sure, get your vet out and have him/her check your pony’s teeth, back, check for ulcers, and everything else to see if there’s any problem. Tell your vet that she’s tensing up and refusing to go to the right more than she is the left, along with everything else she’s doing. Since she’s never done anything like this before, it sounds like there’s probably something physically wrong with her.
If she checks out 100% fine, though, then I would say, as soon as she starts to tense up, before she bucks, not after, take her and circle her tightly. Start out with 3 circles, then if she starts to buck again, up it to 5, then if she does it again, up the amount of circles you do again, even if you get all the way up to 50+ circles. The idea of doing that is, if you start out small amounts and get larger amounts, she’ll learn to respond to the smallest of pressure, rather than the biggest, which is better for you and her, and it will teach her to behave and do what you ask, when you ask, because she’ll know if she doesn’t, then more pressure and more work lies ahead. However, the key is to catch it before she gets too far ahead in her mind and starts bucking, because then she’s in that mindset of “yeah I’m the boss I’m gonna do what I want!” and it’s much harder to get a horse out of that mindset, than it is to get them out of a mindset of “hmm, I think I’m going to buck…” if you know what I mean? Like with my horse, I have to catch him before he actually does what I know he’s about to do, otherwise it’s much harder and often useless to try and teach him to behave if he gets in too dominant of a mindset. Of course, don’t become paranoid, but really learn the signs when your pony is about to buck or do anything, and catch it before she does. Also, always circle her to the left. Since she’d rather go left than right, make going to the left hard, and make going to the right easy and relaxing. Then she’ll learn “hey, it’s easier if I just go right…”. Oh and, when she stops and refuses to move, you can circle her then, too.
But again, only do all of this after you get the vet out and she and your tack checks out okay.