I am saying this as someone who often deals with exclusion in a local authority. I understand your concern and anger. However, it sounds as if the relationship between you/your son and the school may have now broken down completely and is likely irreparable. PX is never taken lightly, schools do sometimes not get the process right but that does not mean you can make everything right by the child returning.
There should be an officer who works for the local authority whose job it is to try to help you think about what is the best solution here- for your son.
Returning to a school where the relationship has broken down may well not be the best thing.
I don't understand, as he is just 13, why he can not start at a new school and get settled and ready for GCSEs at the start of Y10. Why is he only being offered a PRU?
That he is, suggests to me there are serious concerns about his ability to manage in a mainstream school. PRUs are able to offer tailored programmes that are flexible and mix core and other GCSEs with vocational provision . Yes, of course some children are challenging but many are not and make very good progress in very supportive provision where there is access to more support and staff experienced in dealing with issues like ADHD.
When was your son diagnosed and by whom? Surely the school were involved in the diagnosis? Does he have an EHCP? What help does it say he should have? When was it last reviewed? Is he medicated? When was that last reviewed? You need this info to help you in the px discussion and to help you plan his future placement.
It is extremely difficult for a child to return successfully to a school following a px from that school. Other children will watch them and be wary of them or think it is funny to provoke them. Friendships will have moved on. Classes will have made a lot of progress with the curriculum and it will be very difficult to just slot in. Old grudges hang around. It is hard to adjust to being back in the restrictions of a place you feel does not want you back. He is likely to think the school will want him to fail.I have seen it work once or twice but more often than that I have seen it fail again very quickly. It requires absolute commitment, calmness and best behaviour from everyone. I always say to a school in this circumstance they should treat the child as if he/she is their best student- give them every support and opportunity, praise them and help them, be flexible, move mountains, so it stands the best chance. Often the child can not cope with the difficulty or the parent can not cope because they don't trust the school and actually behave in very unhelpful ways.
Please don't go in full of rage - it won't help. What is important is that he is in the right place going ahead, wherever that is.