Yes, other ducks lay in a nest. Rather than have a battle of the wills while you're figuring out the solution, could you make sure she's got food and water close enough so she'll eat more? How about some extra treats?
My runners go broody sometimes and I just go with it. What that means is, I watch for when she leaves the nest, I grab the eggs but I do leave some wooden eggs in the nest so she won't get so upset. I make sure she eats and drinks, and otherwise just let it go.
You're right and good to be concerned about her state of health.