I haven't had this problem, but there are some points I feel you should consider.
How old were your other grandchildren when they started spending a night at your place on their own?
Three strikes me as too young, but if you did this with the others, I can see why your daughter could be concerned that this granddaughter will not form the same bond with you as the others have done.
From other threads, I have realised that the pet in the grandparents' home can become a bone of contention.
Unreasonably so, in most cases, as you are not saying that the dog is more important than the child, but that you are afraid that a young dog who just wants to play could inadvertently harm the child by pushing her over.
Perhaps for the comfort of your other visitors as well, you would consider teaching the dog that she is not a lap dog and that her place is on the floor at a visitor's feet if she wants to show affection.
I am fond of dogs, but I would frankly draw the line at 24 kilos of dog depositing itself on my 56 kilos of woman.
Don't please just say no to your daughter. Sit down and explain why you are concerned that a young dog and a young child might not be the best combination.