How long has she been out of racing? I have found these symptoms to be really common for horses coming out of racing, whether flat or jump racing. I agree with all the suggestions to look for pain: pain or discomfort could be anywhere – neck, poll, jaw, ulcers, even feet. Also, anxiety can come from pain but also from anticipation of “work” and can become a habit, like biting our nails.
For the rooting, I agree with the other poster who said to drop contact when they start. I had a HORRIBLE rooter – he’d root you right out of the tack, Christ, it was awful. He rooted especially hard into downward transitions, so I would ask for the transition with my seat and throw away my reins. He’d root and have nothing to pull against. He didn’t stop altogether, but he became MUCH better and I could gradually keep some contact through down transitions. He had a lot of anxiety.
My friend has a TB mare who ran on the flat for a couple years, really not that long, and she’s now like 15 or 16. My friend hasn’t really done anything special with the horse, just trail rides, jumps around, maybe they’ve been to a couple schooling shows. The horse lives the most chill life imaginable on a lovely quiet farm with minimal demands and STILL she is SO active in her mouth. She flails her tongue, flaps her lips, and chomps constantly. A few years ago, my friend put her in a hackamore to see if she’d ease out of it and no, she hasn’t. Granted, she’s not in consistent work, but it’s been years! At this point, it’s just habit. The mare is naturally “anxious” and ready to work when the tack comes out, despite nothing but super calm rides for almost a decade.
My own TB ran for a long time over hurdles and then hunted for ages. He was run into the ground and has loads of emotional baggage so he’s very anxious. He’s gotten a lot better the past couple years but he still is fussy in the bridle. He has really enjoyed the MB33 dee with hooks. It gives him a lot of tongue relief, which he likes, but still gives me some leverage when he gets strong. It’s work a try as all the bits you’ve tried so far lay on the tongue pretty consistently. The Mylers can be found used but also my local tack store lets bits go out on trial for a week or so, which is really helpful for the expensive ones. Might be worth investigating.
Like others have said, “temper tantrums” don’t come out of nowhere. It’s important to look into this issue, especially if it’s somewhat new. The horse might need some time to chill out and just have calm hacks for a while.