Usually older people have trouble adjusting to ‘the new norm’ - be if changes in their spouse or physical/mental decline in themselves. If mom truly wants both to stay at home, she needs to see some of the things that can be done to help her cope and help dad be able to stay home - be it things like a regular schedule and medications to help him stay calm even if sedating. Making sure he can safely get to toilet on medications. Help coming in that they are comfortable with, with oversight by family and maybe a watchful eye by a friendly/close friend neighbor.
Some situations, no way to keep safely at home.
My mom had dementia but strong will to stay/die in her home (which she successfully did). Brother lived very close and had FT/live in help with her for cooking and cleaning. Mom had a very sweet Yorkie that gave her a lot of companionship. When she had a sharp decline, explained to brother, and brother had her evaluated for Hospice, she had 4 days in hospital on IV antibiotics for gall bladder infection, went home to hospital bed on Thursday and died on Monday.
Having hospice in the end is very helpful in or out of a facility with getting death certificate/coroner sign off.
Everyone’s situations are unique in some ways. I see how families adjust and cope as their senior relatives decline - some who come into rehab and some who come into skilled care (nursing home). Some do move to assisted living - typically a family may see where their senior can manage at AL (and AL evaluates the senior and approves) and they have the funds.

