I agree...this sounds like an issue that may be more resolved by training. Given that she is flighty about her face being touched and a 'certain place' in the ring.
Start taking her to shows JUST to be there...don't show...just take her to the shows, hand walk her around, do some lungeing in areas you know she isn't really comfortable, and wait for her to relax, then just leave that area. When she is behaving better on the ground, then start riding her around the grounds...but again, don't put her through the pressure of being shown...just get her used to the idea of being in a strange place.
Same with her face...the only way she will get used to her face being handled is if she has her face handled, period.
There are supplements that could help her with the anxiety, that won't hurt her...such as Be Calm, and essential oils like Lavander Oil. So if you would want to try something in conjunction, I think it could help for a while, but I don't think it should be something you lean on for the rest of her life...maybe just for a while.
One thing you may want to make sure of, is with the two supplements you are actually giving, that you aren't doubling up on certain vitamins or minerals...too much of certain things isn't a good thing either; not that you would be seriously overdosing, but even just a little of an overbalance could be causing her to be unbalanced in other aspects of her over all health and well being.