I am very wary of posting here after giving advice on a similar thread and being accused of being a jumped up lollipop lady. I'm not a lollipop lady.
I know quite a bit about residential schools for kids with SEMH and have spent time in many.
They generally work to a step-down programme..
Ie their goal is for your son to return to family living as soon as appropriate.
The facilities, rooms, activities, food etc are really good. Children form relationships with their peers and are given intensive help and therapy.
They mainly remain in close contact with family (obviously this isn't always appropriate but sounds like would be in your case) and there are visits home etc
It is an excellent opportunity for your son and the earlier he joins the better the chance for things to get on track.
Please be aware you can visit any appropriate schools (most authorities have a policy of placing in area unless there are reasons such as CSE or County lines) and you can express a preference as to school.
Most residential schools are part of large chains...you can Google and search, meet the principal and Head of Care, look at Ofsted reports.
Honestly I've visited several and they are happy places where children finally get the support as individuals.
This is not your fault...it is just your son needs more expert care right now and so you are getting it for him...sound like an excellent mum to me.