As far as the pulling, I really recommend the Blocker tie rings.
It sounds like, even when she's not frightened, Carolina has just learned that if she doesn't want to stand tied, all she has to do is pull, and either something breaks or you untie her. The Blocker ring will give the same release, except it happens instantly when she gives to the rope pressure, and not when she's broken something. The rings are not terribly expensive, and I use mine all the time on my tie-broke horses for peace of mind. You do need a long lead rope, especially at first, because she may just run backwards for 20 feet. I make my own 25 footers. Lowe's has the best price on bulk rope in my area, but TSC has it as well. Slightly thinner braid can be found at Wal-Mart (don't hold me to it) for something like $16 for a 50 ft coil, if memory serves. Snaps and rope clamps are easy, just be sure to hammer the clamps tight (I like to use 2 clamps, I had a leadrope malfunction once, and now I'm paranoid
), if you have a bench vise, or something to really squeeze on the clamps, so much the better. The only piece of "specialist equipment" I ever need is a blowtorch to melt the end of the rope after it gets cut to length.
WSArabians had a really good idea about getting Carolina to give to halter pressure. Getting her moving away from pressure in general would be really good idea. I personally really like Clinton Anderson's groundwork, as far as finding a detailed plan of attack.
Your mare sounds quite a lot like a gelding I know. He just knows how to throw his weight around, and he's had it proven to him time and again that he's stronger, he's in control. I mess with him every now and again, helping the owners deal with things between trainer visits. He's never won against me, and is fairly respectful for me, but I've also found ways to get respectful responses from him without his getting upset or angry. He can still be a right snot for the owners, but for a combination of reasons, they have a hard time doing what needs done. They do have a pro trainer. Ditto mom2pride; If I weren't so far away, I'd come mess with Carolina myself.