If they could afford assisted living - NO WAY! Best case scenario is a leveled care situation (with memory care available to move into when needed) near your home. Leveled care is a great way to keep as much independence as possible.
I'm going to write a novel, so buckle up!
My parents live in a leveled care situation and they are well cared for. In the last five years we've gone from home help then moving them into residential, then assisted, now memory care as they needed and became comfortable accepting more care. Honestly it's enough work with dealing with their finances and property and visiting them regularly even with them in full care. I retired early 3 years ago because it is so much work. Even having siblings to help, who both also still working when this started and also live no where near them, it was just too much.
Unfortunately, they refused to leave their city/state. If I had my choice, they'd be near me or my sister.
I could never have lived with my FIL - period. He is gone now, so I can see DH's mother coming to live with us if something happened to DH's sister though. She really can't afford decent leveled care. Like your situation, she is in the hospital, now rehab center for a few weeks, and it is touch and go. We're in the process of seeing what she will qualify for in terms of long term care help. At this point, she'll be living with DH's sister and since I'm there in the same town every 3rd week with my folks I can be there to give his sister some respite.
I plan to go to leveled care near one of my kids eventually. I've made them promise to drag me kicking and screaming if they need to because I don't want them doing what I'm doing. Spending all this time commuting between states is not how I anticipated spending my empty nest years! (Though I'm thanking God that my kids were fully launched before this nightmare started.)
I've seen first hand the difference between leveled care and family care because of our two families. I would NEVER choose family care if I had a good leveled care option, especially now that the pandemic is hopefully winding down. My parents have activities, exercise, music, a variety of foods, etc. available every day and then relaxed visits with family (that started again three weeks ago - finally!) . DH's mom has exhausted family members struggling to make it work.
This is overwhelming and it is a struggle. Be careful for your own self care and mental health. It's even okay to feel resentful for this situation. Know that his parents would not want to be a burden and don't allow their current ideas of what is best to cause you to forget what they might have wanted for themselves or for you at your age. Having the money to have options is a true blessing. My parents said early and often that they didn't want us to have to care for them and they would move willing into leveled care - but boy did it change when reality hit them! I have to remember what they used to say, not what they say now.