wellies
To some extent this is not my circus, not my monkeys- but I also know that in all likelihood I will be expected to sort care out when it all goes wrong.
It's not your circus or your monkeys to any extent. Stop aligning yourself with their thoughts.
Imagine this: they think the moon is made of cheese. So what? How does that belief of theirs affect you? It doesn't.
So they expect you to sort out the shit show they're going to create? So what? They can expect it. It's their right to hold whatever beliefs and expectations and opinions they want to.
How does it affect you? It doesn't.
Those beliefs, expectations and opinions are all in their minds. You can choose not to have those things in your own mind.
The reality of how it'll translate into their behaviour is basically going to be insulting you and making rude phone calls where you're ordered around. So what? How do we deal with rude people? Hang up the phone. It really is that simple. You have agency over your own life. They can't make you do anything, including listening to them being rude on the phone.
She says she wants to at least try being at her own home with carers, and going to social groups before discussing them moving in. I don't know whether she has said anything to GB2, but I doubt it would make any difference.
If this is what she wants, she needs to tell GB2, nobody else can do that for her. She can't say "yes" to him and then have someone else come say "no" to him on her behalf so she doesn't have to be "the bad guy". People have the right to make unwise decisions. If someone wants to remain in a controlling relationship, not even social services or the police can step in to disallow it. She has to decide not to have him there and communicate it. Then others can back her up.
What can you do? Two choices -
Walk away... and get shot (metaphorically, by them) for doing so.
Or stick around and help her refuse him entry... and get shot for doing so.
Because you know already that she's going to cave and backtrack and deny saying "no" and tell him "yes".
So, what do you want to be vilified for? Because it's happening either way. There's no option where you don't get vilified and your reputation shot to pieces. It's just a decision between whether or not you put in any further effort before it happens.
In terms of "help" by that I mean you can obtain the name and preferably phone number of your mum's social worker or at least which council (then you can phone the general number to ask for the elderly care social worker department). Then obtain an address or email address for the SW to follow up your phone call with a written trail. Tell the SW that your mum has told you she wants carers and social groups to start with and not GB2 moving in.
When he shows up on the doorstep and she calls you about it, you ascertain that she wants him to leave and has told him this. If she does and has, and only then, you call the police for her explaining that he's trying to move in against her will, she's told him "no" and he's refusing to leave. Let the police sort it out.
If GB2 has sold his house, packed up his stuff and hired a removal van, at this point parked outside your mother's house - that's not your problem. That's his problem because he shouldn't have done any of that without first definitely ensuring he has somewhere else to go. And deciding unilaterally to move into his mother's house ain't it. It's not something you have to get involved with. His stuff can go to a storage unit and he can go to a hotel, until he either buys another house or rents another one to live in. You don't even have to have that conversation with him. He's an adult, married to another adult, and they can work it out for themselves.
Contacting SW and police, that's you advocating for your mum, which is realistically all you can do. If she backtracks to these people and tells them it's ok for GB2 to be there, you need to accept that as her choice and stop worrying yourself about it. Because your mum has agency over her own life too, should she choose to exercise it, and there's nothing you can do if she doesn't.