This sounds very stressful.
Your dm is obviously a hoarder. She will not be able to allow someone to take control. This is how her brain works. To non hoarders, we see the 'stuff', we can easily say bag it up, store it, throw it out. To a hoarder this is their life's precious possessions.
A hoarder will want to keep their things in the home. Unless they have reached the point of wanting to get rid of some of it you'll have to work around it and come up with a plan to make some space.
Your brother obviously knows his dm is a hoarder, he will have told his partner. His partner will know it's more than untidiness.
Speaking from personal experience, when I couldn't get a hotel when visiting my parents and had to stay with them, I arranged one bed room, the sitting room, the kitchen. The bedroom I would stay in I would move the stuff out off to another room, same with the sitting room, move stuff to a spare room. The kitchen I would wash and sort dishes and make enough space to cook. Anything I moved into a spare room I would then lock that room. I would then air the rooms and put fresh bedding on, give it a good hoover etc
It's overwhelming for a hoarder to have their belongings touched, it's overwhelming for them to do it. It's overwhelming for them to watch it being done. You need to explain that you're just temporarily moving things and will move them back. You're not throwing anything out.
By just doing a couple of rooms, enough for your brother and his family to stay, it won't take as long and they'll have a room they can stay in comfortably.
I wouldn't be giving up beds and rooms, you could assemble the bed and put in a high air bed, there's fantastic air beds out there now. The child can sleep in with the parents on an airbed. Buy a small TV for the bedroom so that they can go there for their own space. Tvs are really cheap now and they can watch Netflix on it.
The main thing is, once there's enough space to move around the rooms they'll be using then it will feel better. It doesn't matter if the walls are lined with possessions. Sometimes when we think of hoarders we think of those programmes on TV where they're climbing over 6ft of stuff, but there are hoarders who just keep everything and stack it in any space available meaning they can never clean properly or have it looking tidy.
Once your dm sees the progress without having to throw her belongings out she will be OK. She probably won't while it's happening and there'll be arguments etc but I always found not working at a really fast pace, showing I was careful and respectful of their belongings and explaining what I was doing helped.
Good luck with it all. I understand the stress and it is very difficult to deal with.