Just one contribution from experience, the language barrier won't stop care home staff from doing their job. It would work even if she knew no English. Especially in a dementia home where any of her demands would probably be based on fiction and be unreasonable anyway.
Given that she is likely to not know where she is, it is far better to be near family. You can be reached in case of accident, illnesses requiring hospital admission, and you can help with the English in these cases.
I also think that the children aren't responsible for the costs in the UK?