If the admission criteria are as you describe they are clearly in breach of the Admissions Code.
Children of staff can be prioritised but they cannot be placed first. LAC children must come first.
If SEN children means children with a statement of SEN or an EHC plan naming the school they should not be included in the oversubscription criteria at all. The school must admit such children even if they are already full. If it means children with SEN that don't have a statement or an EHC plan they cannot be placed ahead of LAC children.
There must be a category for LAC children of the faith which must be the highest priority for admissions.
The letter is also in breach in that they are required to set out why you didn't get a place. Simply stating that you haven't got one is not good enough.
If you would like to PM me with the name of the school and LA involved I will check it out and let you know whether or not they are in breach.
Unfortunately being in breach of the Admissions Code only helps you if your child would have got a place had the admission arrangements been correct. So the real question is whether the breach led to other applicants wrongly being given priority ahead of you. If you PM me with the details I will be happy to give you an opinion as to whether or not you have a case on those grounds.
An appeal on the grounds that the admission arrangements were incorrect is potentially a very strong appeal. However, that may not work out so you also need to prepare a case as to why your daughter will be disadvantaged if she doesn't attend this school. Look for anything this school offers that isn't available at the allocated school and which is particularly relevant to your daughter.