Enchanted,
I have two dogs ( a golden and a Saint Beernard/Great Pyrenees mix, both of which, only go out on chains and never would touch the eggs, even if they could reach them. I also have two cats, one is strictly indoors, and the other older cat goes outside, but he is a big baby. Sweet as can be, in fact, he used to lay with our other ducks when they were ducklings inside the house last year. So I have serious doubts that he had anything to do with it.
As for kids, I suppose it's possible. The eggs are in a spot that is very difficult to reach inside their pen. We have an L shaped pen, with doors on each end. She made the nest in the middle, and without crawling inside, it would be impossible to reach. But it IS doable I suppose.