Which bit don’t you understand?
We will appeal the decision, but if the school say they are full, I don't think we can contest that.
Unless the school is wholly independent, this isn’t correct. You only need an offer of a place if the school is wholly independent.
Unless wholly independent (is it?), your preferred school must be named unless the LA 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.
Being full is not defined in law, and on its own being ‘full’ is not enough of a reason to refuse to name your preference. The LA has to prove the school is so full admitting DS is incompatible. The bar is higher than many LAs admit. It is more than an “adverse effect”, “impact on” or “prejudicial to”. Unless the school is wholly independent if one of the above cannot be proved the school can, and must, be named regardless of the school’s objections.
I thought in order to be entitled to ETOS, they have to have failed multiple provisions
This isn’t the case. The legal bar for EOTAS is if it is inappropriate for the provision to be made in a school. It is possible to get EOTAS without failed placements or even attending a placement at all.
If you haven’t already, have a read of IPSEA and SOSSEN’s websites to understand the EHCP process better.