Because tone is impossible to convey through text, please read my reply to you as if it's coming from a loving friend, as that's how it was written. 
I think you should start saying "thank you" to your eldest daughter, try maybe once a day.
Telling her not to come by for a period of time isn't really showing thanks, though I can tell it was your genuine attempt at doing so. But all it (her taking a break for a bit) would do is temporarily stay the work she does and let it accrue for her to take on at a later date. As when she begins caring for you again, I'm assuming she will need to, in addition to the usual routine, do all that was put off. And she will also need to tend to any problems or complications with your health that arose in her absence (not good, your health is important). Which, I think would be sure to occur, due to, as you have said, the quality of care she provides is unable-to-be-matched.
I very much understand that you were trying to show appreciation by telling her to relax and take a break for a while, however the reality is that it, in practice, would not be good for either of you. You, in the immediate sense, regarding your health; her in the long-term, regarding what I wrote above. So please, look her in the eye and lay a gentle hand on her arm, and say "thank you". It would mean a lot to her, and I think to you too.
I wish you the best. Take care.