If she is that active there is no reason to go to a nursing home at all. If she is more like a skeleton, needs diapers, to be washed and so on, I bet her daughter will not have the energy to take care of her on long term.
I wonder if it isn't too expensive and too late to start saving for a nursery home. With us it is: the more money you have, the more you pay and it isn't said you will be looked after better. They simply lack the caretakers. Waiting half a day for someone to help you get on your stockings is better at home trying yourself instead of in a room of 3*4 where they tell you to go to bed at 8 pm
That's exactly the point, needing someone to bathe you, to do things you used to do yourself. I don't like depending on other people. I've learned to be independent and it will be very hard for me to have someone taking care of me. That's why I work, so I can pay them well for that job. Honestly, imagining this isn't pleasant, but it's another stage of life.