At the moment her needs aren't being met as the focus seems to be on what she wants.
Such a frustrating situation. I know you commented on similarities between your MIL's situation and mine, and it is so hard standing on the sidelines when you know the issues and can see what you think is the right path. At least your husband can see that a care home is needed - I'm not sure he did a while ago.
I think my husband can see more clearly what will be needed with his mum too, but we have other issues beyond that.
My MIL is not as far along as yours - but we know things can happen quickly.
The poo incident that happened early in the morning could easily be repeated at any time of day, and for MILs dignity she needs someone there 24/7, she was clearly aware of things to some extent.
But you and your husband know this. It's finding a way to persuade the others.
If SIL gives up her job will it leave her stranded without a source of income if MIL then goes into a care home? If it won't leave her stranded I guess it is worth a try as it's better than it is now, but then a whole load more difficulties might present themselves.
Grannie G has listed a few points that are very pertinent to this situation, which if possible need to be aired between the 4 siblings.