Hello OP, I haven't read the whole thread so apologies if I'm repeating things others have said.
I can completely see from your description of your daughter's needs that a mainstream secondary is not appropriate, and as a parent of children with additional needs I can completely understand your very serious concerns about sending her there.
It's unfortunate the appeal date has passed, but I do think you can't be the first parent in this position and others with more experience may be able to advise you.
I think you're right to listen to your gut and not send her to a school you are clear cannot meet her needs. However, I also think the strain of electively home educating a child with high support needs is something to be very very careful before you do it, because once you electively home educate, the EHCP ends and it would be very difficult and time consuming to get one again in future if it turned out you couldn't meet her needs at home, and then also run the home and look after your other children (none of us is super woman!)
So, I think you need some proper advice.
Can I suggest two things?
Firstly, could you get this post moved to the SN Chat board here on MN? There are some amazing and experienced posters on that board with a tonne of legal knowledge and they could advise you.
Secondly, there is a FB group called EOTAS. Another place for lots of good advice. EOTAS stands for education other than at school, and it means your child being taught at home (if there is no school that can meet their needs) but funded and resourced through an EHCP by the LA, eg the LA pays for a specialist tutor / speech therapist to come to your home and deliver the education.