Actually, she's a fruit loop. You can be riding, she'll be going beautifully, or just walking or anything and then you're either on the floor or in the middle of the school wondering how you got there.
Without more info only an educated guess, but it sounds like she may be extra sensitive & has either not had enough training or got enough trust in her rider, or she may have had incorrect training that has exacerbated her fears. Either way, paying attention to her, so that you catch her responses that come before the spook should help you be ready for it & stay on when it happens & also help her gain more trust in you. After all, if you're not paying attention enough to notice her worry, how can she trust you to look after her in such events?
Every time you get a rug down, or put one up, she completely freaks, and starts to shake. Once the rug is down, no issues
Horses learn by association, so either getting a rug down somehow hurt or frightened her, or something else hurt or frightened her at the time someone was getting a rug down.
Continuing to put her in a confrontational situation where she feels she must fight for her life is only further confirming her fears & if you are associated with this too, will make earning her trust much harder. So I'd advise first & foremost, quit tying her there, for now at least. Instead I'd find a place far enough away from the rugs that she can handle without panicking and with repetition & reinforcing her calmness, ensure she's actually comfortable with rugs coming down at that distance first. Then gradually ask her to come closer & ensure she's truly comfortable at the new 'intensity' before you go closer still.
I wouldn't tie her up or try to hold her tightly during this process, as this will cause her to feel trapped & more vulnerable, making panic more likely. In fact, through association, she may now have developed a bit of a tying problem, so you may find that's another part of her training that needs attention. Again, don't force the issue, but work gradually & non-confrontationally towards your goal. I find using a long rope wrapped around a rail, or using a 'Blocker Tie Ring' is effective, because if/when the horse panics, they aren't stuck, but can move their feet and put slack in the rope. With repetition & gradual increase of 'hold' on the end of the rope, you can teach a horse to *confidently* stand tied.
We tried the 'stop being silly' thing, backing her up, making her stand firm with her head down, but she's just crazy over it!
She's not 'being silly', so trying to punish her for it won't help. Imagine being in a foreign country with people you don't understand trying to force you to put up with something that terrified you. Now put yourself in the foreigner's place & think about how you could go about convincing that person that you're trustworthy & the 'scary' thing is actually safe.