Hi pregnant,
I feel I had to respond to this, as my MIL is 6 weeks into a care home (mid-stage Alzheimers) after point blank shutting down all other at-home care options which until then she'd been very accepting of. She'd also become a danger to herself in a number of different ways I won't bore you with here. Like your mum, she also had a cat that she lived and breathed for (now with us).
MIL is also very articulate and capable in many ways - but an absolute risk to herself in many more others. Unfortunately dementia isn't a flat decline in this respect...
It has been a long five years caring for her, an agonising 6 months fighting just to get SS to acknowledge she was at a point that full-time care was needed.
We are fortunate OH is an only child, as if a sibling had tried to block the decision (hard-won, and long agonised over) I think the relationship between all of us would have entirely broken down, particularly if that sibling was less involved in day-to-day care, or more "in denial" than OH and I at that point (not saying that is the case with you - but believe me, I understand the denial stage all to well!).
OH and I were at utter breaking point by the time MIL - far too late for her own good and not before a final night flooded out of her flat after blocking the toilet flushing down rags - was finally moved. I seriously think one or both of us would have broken under the strain had it carried on even just days longer...
If your DS is at this point, it's important you listen to her, and don't hold her hostage to your sentiment that "you promised" your mum wouldn't go into a home. That is a promise made only by those who don't understand the sheer impossibility, and agony, of caring for someone with dementia long-term - and with cancer in the mix as well, her needs are only going to increase.
MIL is adjusting slowly - I won't say it's been a pretty 6 weeks, but she is getting there. The cat - the point we worried about most in engineering the move - she hasn't mentioned once!
Btw, MIL had an understanding of what a hospital and a care home were too - that in itself does not equal mental capacity, but rather being able to weigh up risk to oneself if one goes in / does not go in, and logical results of that decision, etc.
I sympathise with your DS, who as POA has likely taken the responsibility of care home viewing (which is a horrible process, btw) on her shoulders, in order to spare the other siblings going through it. She is not making the decision without you, only informing you that she has done the research.
I only wish someone could have done all of the above for us!
Maybe I'm projecting my own situation a bit here, but I'd strongly advise that you listen to your DS on this one.