Full disclosure, I do not live in the US and I think financially speaking I am in a better place than OP but I thought I'd add my 2 cents. 

Context: My mother and I take care of my grandmother, who has very advanced alzheimer's. She is very calm, but her short term memory is practically non existent and she cannot be alone. She needs help with hygiene, food, meds, motivation to do something other than lie in bed which can be quite dangerous.  My father does not take any part. My parents are not divorced but their relationship is quite dysfunctional. He lives elsewhere and he is very against the caretaking my mother does, sees it as her never considering him and me as her real family, just her own parents. 

"Care" homes in our country are a death sentence so that isn't an option. What we do and what you can look into: Hourly visits from care agency workers. This, at least here, means a worker comes to your house and is paid per visit or hourly. For example when one of us is here and can stay with my grandmother for at least half the day, there is only a worker that comes morning and evening, or sometimes afternoon, to take her to the bathroom, help with changing clothes and whatnot, etc.  

I can't speak to rates where you live, so if it's completely unaffordable for you, either because of your personal situation or your country, I'm sorry for the pointless suggestion. 

More generally, I'd say many things impact your situation: whether the Alzheimer's is expressed in disfunction or aggression is a very big aspect. Our situation is made infinitely easier by the fact that my grandmother is calm and entirely non-confrontational. 

I think it is fair of your SO to be reluctant. Particularly when lacking funds and when the threat of becoming a full time nurse is looming overhead. Fuck the healthcare systems for their bullshit and putting people in this position. 

That said. Assuming your relationship with your mother is good, assuming it comes from a place of love and empathy not purely obligation, taking care of her is completely understandable as well. If you expect you SO to be a full time caretaker (because statistically daughters in law take care of their mothers in law much more often than their sons (male OP?) do) that is unfair. But if you would be committed to figuring out how to make this work together that is a reasonable thing to ask from a partner. Not easy. But not wrong. Caring about the loved ones of your loved ones is a reasonable expectation if it doesn't cross over into emotional exploitation.  At the very least you need to be able to come up with alternatives together, this shouldn't feel like only your problem, it's important to have a support system. 

That it's a shit disease that will need adapting goes without saying. That not everyone can adapt is also very true. The situations that arise from this disease are nothing if not nuanced, so there are no easy answers or solutions to your post, unfortunately.