"They'd never have put me in a home"
A particular sentence, said in the head or said by an aunt, and it carries a lot. The generation before you looked after their own, the argument goes. Gran lived with them till the end. They'd never have done what you're considering.
Some of that is true and some is a story. Brody, who spent a career studying what she called parent care, argued in 1985 that caring for ageing parents had become a normal and expected stress of family life, and that the idea of a golden past in which families cared for their old better than we do was largely a myth. People didn't live as long, so parent care lasted years rather than decades. Fewer women worked outside the home. And more of what happened behind closed doors was hidden than is now.
But suppose the sentence is true of your family. Gran did live in the back bedroom. Your mother did do it. What follows? Your mother did it in a different life. Different jobs, different distances, different lengths of illness, a different number of years between a parent's first fall and their last. And, quietly, you don't know what it cost her, because she wouldn't have said, any more than you're saying now. The generation that looked after its own is also the generation that didn't talk about what it was like.
Then ask the real question, which is not what they'd have done but what they'd want for you. Very few parents, asked plainly, say they want their child to give up their health and their marriage to keep them out of a home. What they say is that they don't want to be a burden. That sentence is usually sincere. It's also the mirror of yours. You're both trying to owe less to the other, and neither of you is saying it, and the arrangement that results is one nobody chose. Chapter 21 is partly about saying it.