My mother-in-law in unable to care for herself. She refuses to get out of a chair at all. She does not want to go into assisted living.

When I told my dad I had a certain AL lined up for him and mom after rehab, he said, "wow, that's a really nice place! Thank you!" So much for nobody ever wants to go into AL, which is like a nice hotel, in reality, with ones own spacious apartment. And on site caregivers IF needed. "Poor souls" who have the finances to live that way, huh?

When you tell MIL you'll no longer be her caregiver, ask her what she plans to do next?

I don't think there's ever been a person who wanted to go into assisted living, or a nursing home, or a memory care facility.

If you can't or do not agree to meet her care needs anymore, others will have to. So get APS in to assess her situation and you tell them you're not taking care of her anymore.

Then you take a great big step back and let them do the job they are getting paid to do which is make sure vulnerable adults are living safely and receiving adequate care.

No one wants to go to ALF.
At some point that isn't a choice.
I would also be clear that many ALF will not accept someone who is w/c bound, while many others do.
It seems it is time to discuss with hubby and be honest then with MIL. Tell her you are not up to caring for her in this condition and will assist her in seeking placement. No argument, no discussion. Simply one and done, and then help her with this stage.