Has she definitely been turned down for a Special school place?
LAs can vary but usually the process for Special school applications is that cases go to a Panel and then you get a letter telling you the outcome and what steps you can take next, e.g. appealing.
This is separate from and trumps the general admissions procedures for Year 7 transfer. For children with EHCPs, these have to be completed by mid-February, so slightly earlier than Offers day. Children therefore won't be without the offer of a named school place if their case has not been heard at Panel by the deadline.
Contact your LA SEN team and ask when your application for a Special school place is being considered. (Unless it's been heard and turned down, in which case you would have had that in writing, along with information on how to appeal).
If her case hasn't yet been heard, then accept the place offered, even if you don't want it, as the LA will have fulfilled its duty by offering a place and, as PP has said, it becomes more tricky to work outside the system.
If she gets a place at Special school, this over-rides the offered mainstream place, which will then be offered to the child at the top of the waiting list. If she doesn’t get a place, then you can still reject the mainstream place later if you decide then that you will home-school her.
If her case has been heard and the place refused, are you still within the time-scale to appeal? If so, then do that, unless home-schooling is your preference above Special school.
If you're out of time, then you'd need to find out what the LA policy is on re-applications. Chances are that there will be a time within which they won't accept them, and/ or they won't accept without new evidence.