Your family might have Muscovy ducks, they are not very destructive and usually just lazy. Mine sit around for several hours a day. They only take baths a few times a week and they do not know how to drill like a mallard derived duck. When Muscovies do get up they usually wander around in the grass and grab bugs, fruit, and pull seeds off of things.
The grass will be nonexistent wherever you have water with MD ducks. They also run around a lot more and sift through the grass with their beaks to get bugs. The grass is not destroyed from my MD ducks though it is just a little short in the area around the chicken coop. I have lots of poultry that will free range in this area, 70 chickens, 3 turkeys, 9 MD ducks, and 10 Muscovies. So I can't really blame all the destruction on the MD ducks, but I know they are responsible for all the mud by the water and all the little holes all over the yard. Oh, I also have a large kiddie pool out for them, there is no grass 2 feet out from the kiddie pool and there are a ton of drilling holes everywhere.
I have never really had problems with any poultry destroying grass, I don't know if that is because I have 75 acres that they free range on or if it is because my definition of destroyed is different from everyone elses. To me, short grass around the coop, a few small and shallow holes in the ground, and a small amount of mud is not destroyed grass. It might be because of space too though, out of the 75 acres the ducks, chickens, and turkeys only use around 10. That is still a lot of space though and they are to scared to go any further. I am sure if you had them in a small fenced in yard they would kill every plant in there.