My mum lived with us for the last 10 years of her life (died at 84). It can be a delight and a privilege and really useful, as it was with mum. None of us ever resented her presence or involvement, but she was careful not to interfere unreasonably though that didn't atop her frequently telling me I was wrong! We had a good relationship with her; dh wished often that she had actually been HIS mum and dd adored her.
It doesn't sound like your sis finds having your mum there is like that.
You each need to have a chat with your mum about what SHE wants, why she's refusing the help on offer - especially the nebuliser. Does she feel that it would just ge easier on everyone if she collapsed and never came round again or something awful like that? If so, who is making her feel like that?
I know that at 84, mum felt it was time for her, that she'd had enough of being old, so when she was dx with cancer she rushed off to the doc and got herself a DNR notice. Her cancer was inoperable by the time it was dx, but she'd hung back on purpose really as she wanted it over and done with. It was, in a few months. Left us broken hearted and in shock, but I could see her point. There comes a point where increasing disability just becomes so booooooring (approaching that point myself).
So you need to egt there and talk to your mum. It can't be impossible to talk to her on her own in her own place, or in hospital, without sis or horrid husband butting in. With a bit of advance organisation and a crumb of cunning....