It sounds infuriating that your daughter hasn't been given the help she needed despite all your pushing. It shouldn't fall to you. However, I you're wise to look at Plan B in which you do some of the organising yourself.
I agree with @QueenofTheSlipstreamVM that you can reduce the pressure on yourself and on your daughter by re-thinking the big picture. Given what you've said about school being able to provide an exam venue etc, it does seem ideal to sit some exams there in the spring. However, the upside of your situation is that you can pick and choose which exams to access there. If eight subjects is too much work and stress, your daughter can do five. Or three. If she doesn't see the point of RE, drop it. Most home educated kids sit fewer GCSEs than school pupils, typically just the minimum to get them onto the next level of education or employment. Five or six is plenty. Schools have targets to meet. They want kids to get as many exams under their belts as humanly possible, even when that isn't in the best interests of the individual child. Also, it is very common for HE kids to spread exams over a longer time period, so if she can only do a few this year, she could do a few more next year - if not at school, then independently.
Reassure her that there are many ways forward. Knowing that will help her weather the stress of sitting exams. Too often at school, teachers go overboard with trying to impress on kids the importance of doing well in their exams. For some children, that is the right approach, but others become paralysed with fear and it just backfires.
Going easy on exams doesn't equate to getting an inferior education. Your daughter can be learning things which don't lead to a qualification but DO achieve the ultimate aim of education. GCSEs are sometimes useful, but they do not equate to a good education.
One of my kids, who had a chronic illness and anyway didn't particularly want to do exams, learned various subjects including art in their teens. They sat English and maths GCSE aged 19/20 and then went straight to university to do an arts subject, where they are excelling. One admissions tutor described them as "the most impressive candidate I have seen in my five years in this department". I actually think that if they'd been dragged through a succession of GCSEs, they might not have had the time to develop the other skills which landed them a place at their top choice uni to study the subject they loved.