So the set up with your second daughter would be that you live with them and give all your pension into the family pot (do your daughter and her husband have joint finances then?)
And in return they provide housing, food? clothes? transport? life admin? Cooking? Cleaning? Shopping? Personal care?
Do they have room in their house? Will your bedroom be the existing spare bedroom, or one of their children's rooms meaning they now need to share? Do they have space they can convert to an annex - who would cover the cost of that?
I think you should have a very frank conversation ahead of moving in, to make sure this doesn't fall apart in the future.
People from different cultures will have wildly different expectations on this. And people from different cultures who have lived in the UK for a time and have made British friends/been exposed to British opinions of looking after parents in old age, may have shifted in their expectations - ie this daughter and her husband may not be as open to this as you may expect from their upbringing.
What level of care do you expect them to provide with their own hands? What would be available to you from the state? What can you buy in?
It is transactional, but what chores are you able to remove from them now - cooking? Cleaning? Childcare? How do they benefit from the arrangement?
If you have property in your home country and no intentions to return, why not sell it now to help fund your old age here? You could give a small gift to both daughters, keep the majority of the capital to invest and use it as an additional income to supplement your pension.