@glasswings at the moment it sounds like SIL is as much part of the problem as MIL. I am guessing that SIL is soldiering on as it is easier, in the short term only, than having the conversation with MIL.
For MIL 'keeping it in the family' is a way of pretending she is still coping.
SIL has fallen into the boiling frog scenario. It starts as a little bit of help and support then slowly grows to full time care.
I do think that once independent continence is lost the next step is care home. Are there funds to pay for this?
Is there anyway that SIL could be persuaded to go away for a day? Be out of sight while you and other SIL have a stern conversation with MIL. The two of you be the bad guys.
You also need a firm conversation with SIL. If MIL is bedbound she needs profesional care. Turning, moving, equipment and training to avoid injuring herself and MIL.
Again you and other SIL taking the role of bad guys to hammer the message home.
Not being able to see the reality of her situation was one of my DM's earlier dementia symptoms. She did use her upset (screwing her face up and pretending to cry) to try to manipulate DB/me into 'taking her home'.