Runner knowing what to do for the best is always difficult. Often there isn't an option that is 100% perfect, you can only choose the best option for you and DD.
Zoo DD does have SEN, SEMH is a type of SEN. DD would meet the legal threshold for an EHCNA of a) has or may have SEN, and b) may need SEN provision to be made via an EHCP. GPs can do school evidence, but I would focus on getting it from CAMHS.
You can appeal the school named in DS's EHCP, the LA can't do anything to stop you appealing. Don't let them pressurise you in to not doing so if you want to. At the moment however, you can't deregister DS without asking the LA for permission as he is currently in a SS. A formality, won't be refused unless safeguarding concerns.
Unless the school is wholly independent the LA can only refuse to name your preference for one of the following reasons:
-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 is high. Case law shows incompatibility is more than an adverse effect, impact on or prejudicial to. There's no legal definition of full. Being 'full' is not enough of a reason to refuse admission, the LA have to show they are so full it is incompatible. In what way do they say they can't they meet DS' needs, do you agree? The LA can, and must, name a school despite its objections if they can't prove one of the above reasons.
Is the ARPs primary need SEMH or ASD? Can you go and look at/speak to the mainstream the ARP is going to be attached to? If you wanted to challenge it you can, with even half the needs and provision that should be in the EHCP you would have a good chance at tribunal.
If they are opening September they must have already recruited staff and even if not finished the accommodation must be planned at least. They must also be working on a model of how they expect the ARP to work. They should know how many pupils, what subjects, the proportion of time expected to access mainstream etc. They won't know transport details yet, they are always last minute. Information may be available on line from the consultation when the LA decided which school to place the ARP at.
You could have challenged DS receiving inadequate provision over the last 2 years.
DS will get transport, nothing to do with you not driving, everything to do with DS's SEN. We choose to have mileage instead for DS3 because we take/pick up DS2 anyway.
From your posts I believe you would qualify for legal aid should you wish to appeal.