Go through with the appeal, but bear in mind that future employment may be challenging.
While references are written, there are so many phonecalls between heads about staff off the record, that even if it looks like a sure thing, a single call can wipe it out.
Your partner should have been informed at every step of the process that she was going to fail. Her tutors at university should be able to offer advice, as should her union.
Can’t abide by bullying heads. Although they did inspire me to become one, a head, not a bully.
I stood up to a corrupt system, and ended up being told to move on or be moved on. I chose to move on and got a glowing reference as it was international. If it had been local or UK, I suspect it would have been very different.