I, too, think the title is quite a bit different than the question in the OP.
In the OP’s situation as described, I would say No. Two, one with dementia, one with mobility issues, in hospital now, your working full time, and their having the money to go to assisted living - that makes much more sense.
Our situation was different. My DH is a saint, it was his idea for us to put an in-law apt on our house for my mother. Honestly, it was easier at the time than what we were doing, which involved traveling to help her deal with a lot of issues after she was widowed, which was difficult given our location and work schedules, etc. She was also relatively young and mostly independent, so for about 25 years things were fine.
Well into her 90s she became ill and also broke a hip. We did care for her at home through her passing, but I am a nurse and my daughter at the time was a senior in nursing school, so between the two of us, with support from DH and DS, we were able to manage all of her care at home. And I’ll agree with others, it wasn’t easy, and sometimes I wonder how we made it all work. But we have no regrets and we felt fortunate to be able to do it for her. She helped us when our kids were little so it felt like the right thing to do, ie give and take. She was also a good patient and wasn’t too difficult to care for (aside from the occasional
if she was unhappy about something, lol). Mom was a caregiver herself, so it all felt pretty natural to us. And DD learned a ton about caregiving during this time. Toileting issues are always tough, and trying to get someone in a shower who is dead weight, and someone being unable to walk very well but still getting up, with falls, or someone eating, but choking, well...that decline was probably the hardest stage, both physically and emotionally. Once the hospital bed and lift were delivered, it became a little bit easier, both physically and emotionally. But I do think that it would be very difficult, if not impossible, to manage these things without a background in nursing and several people available to help 24/7. And even with those things, no one could really fault someone for not being able to take it on.