DM must be absolutely exhausted.
I think it would be worth considering how you see this playing out if you do want to insist on your father having home care, and your DM persists in her wish for a care home. I mean, she just may not agree to what you are proposing - and as someone living in the house, that is her right. (I think one must accept that having him in the house, even with carers, and even if the house is divided, will undoubtedly perpetuate the very heavy mental load she is bearing - unless ‘divided’ basically means significantly restructured into two completely separate houses, which would require planning permission, building work etc, and unless you and sister take on all administrative responsibility for your father’s ‘divided’ part of the house, bills & maintenance etc and organising his nursing and medical care.)
Would you, instance, go so far as to report DM to social services, if she progresses the care home idea, on the basis that she is not acting in DF’s interests? What would happen if she simply refused point blank to live with him and the carers (as is her right)? Is the house jointly owned? If so, she could presumably insist on sale, to fund a new home for herself free from him. Or, would there be sufficient funds for her to move out and buy a new home, leaving him and the carers in the large home?
When you start working consequences through like this it all sounds extremely unpleasant; I would have thought a move to the care home, in accordance with DM’s wishes, would provide a much smoother end stage to your father’s life and their marriage without any potentially devastating family conflict.
Plus - and I’m saying this as someone who cares for elderly relatives- I would not be at all happy at intervention from someone who has not borne that daily burden and who does not fully understand the complexities of end stage dementia, how devastating it is, and the level of care needed and the mental load. I think you need to tread very carefully & with humility in this context.