This is one of the most heartbreaking stories I have read on here. This isn't about Airbnb, this is about the fact that your daughter has been taught that violence from males is something that women have to endure and work around.
So should her future partner start beating her when she is older, instead of calling the police, she may well think to herself "What can I do better to make sure he doesn't beat me again next week?"
If she came to visit you in floods of tears with a black eye from her boyfriend, would you send her home and tell her to wait, give him some money next time it looks like he's going to kick off, and see what happens over the next year or two?
The situation with your son has long since passed the point that you can weather it out and hope for the best from SS.
If you throw him out, change the locks and inform the police and SS, SS will have to step in as your son will be a homeless minor.
It won't be great, and he may end up in a hostel, but right now you and your daughter are living in real physical danger, in a terrible environment - "The cupboards have no doors,there's wholes in the walls,wall paper ripped it's absolutely trashed and every time we fix something, Ds breaks something else." If he ends up in a hostel because he caused this situation, then so be it.
I know you feel you are doing everything you can, but you are letting your daughter down. Spending money on an Airbnb is not helping. It's giving her a teaspoon of Calpol instead of taking her to hospital when you know she has pneumonia. The only thing you can do to help her - and she should be your absolute top priority above all else - is removing your son from your home for good.