Regardless of how much you love the children, the crux of the matter is how you will cope with looking after them, especially when you are not used to it, and given your health problems. My advice would be to have a dummy run. You have time between now and 20th Dec to see how you get on.
Three year olds, however well-behaved, can be a real handful, especially if they are put into a situation they aren’t used to. They need to be played with, cuddled and fed. The baby also might be unsettled and demanding. You don’t say so, but I get the impression you don’t have the two girls together, and maybe don’t have the baby on your own at all. So they will be coming into a new situation. Is there anyone to be there with you? You don’t mention a husband or partner.
Of course, both children will be older by the time you have them, which may, or may not be a good thing!
Given your arthritis etc., I think your daughter is asking too much of you. How will you lift the baby? If she won’t settle and needs cuddling, how will your arms cope?
It really boils down to how you feel. Are you confident you can deal with a small baby and a fretful toddler?
I would do it, but then, I am used to it, having done it on and off for thirty years! My youngest grandchild is 17. I also have a great- grandson who is 6 months old. He is a good baby and I adore him, but I would not risk having him here on my own at my age (80) and with my health problems, even though I am able you lead a normal life.
To be brutally honest, I think your daughter is putting you in a very difficult situation. One which, in your position, I would probably refuse to go along with.
One thing has occurred to me……if you had the 3 year old, is there anyone else who could care for the baby? Maybe a friend of your daughter’s, as you say there are no other grandparents?
I wish you luck, but please don’t do anything you’re not comfortable with.