Presumably DD has an EHCP? When you move LA the new LA must review the EHCP within 12 months of the previous AR or 3 months of the EHCP transfer, whichever is later. Following this review you will get the right of appeal, so you don’t need to be stuck in the current school. Have they reviewed the EHCP yet?
Why is DD not attending full time? If you feel DD can attend full time but the school say she can’t they are illegally excluding her. In which case inform the school in writing DD will be attending full time unless they provide formal exclusion paperwork. If she isn’t attending because you don’t think she can cope attending full time, the LA have a statutory duty to provide a suitable, full time education under s.19 of the Education Act 1996 and anything specified and quantified in s.F of the EHCP. In this case you need to email the Director of Children’s Services requesting provision and threatening Judicial Review.
Unless the school you want is wholly independent the LA can only refuse to name your preference in the EHCP if they can prove:
-The setting is unsuitable for the age, ability, aptitude or special educational needs (“SEN”) of the child or young person; or
-The attendance of the child or young person would be incompatible with the provision of efficient education for others; or
-The attendance of the child or young person would be incompatible with the efficient use of resources.
The bar to prove the above is high, much higher than many realise. Unless the LA can prove one of the above they can name the school regardless of whether the school objects.
Do you have evidence mainstream can’t meet DD’s needs and that she needs a SS or ARP?
If you want mainstream you have a right to it, although not a right to a specific school, unless the LA can prove it is incompatible with the efficient education of others and there are no reasonable steps that could be taken to remove the incompatibility.