My family is not getting along :(
First - just be sure no one can get to the ducklings. Ever. Job number one.
Then - each animal is unique - - - sometimes they don't get along.
But, there are many cases where it works out. But safety first.
I did not introduce my cats to my ducklings until after the ducklings were taller than the cats. They are not good buddies (the ducks don't like them, much), but they coexist with no problems.
Dog trainers would have some more information for your dogs and how to train them. You ought to never leave them alone together, from the sounds of it. But you may be able to train the dogs to "leave it." when it comes to the ducks and cat.
Thank you for your response. It gives me hope. My ducklings are in a cage and when I take them out the cat is in a room with my children. I did find out today my cats little paws fit into the cage which did give me a scare but I never leave them alone knowing that. I will give them some weeks of growing before giving up completely.
I recommend getting some plastic poultry fence with small openings. I did that for my ducklings' crate because my nightmare was moving the crate and a duckling sticking her neck out and it getting broken.