Hey,
Ducks do sometimes get runny noses, and to clean them they must be able to submerge their heads/bills in water. Unless this is constantly happening, or if the discharge doesn't turn to a funny colour, then i wouldn't worry.
What are you feeding them? Mixed corns, grains, and starter foods are fine. Don't feed to much bread to young ducklings as it swells up inside their digestive system. They also love natural and green foods such as grass, worms, lettuce and dandelion leaves.
If they cough/spit after eating, it could be beacuse their eating to quickly. Try feeding them very small amounts (little and often) so that they have time to swallow and digest their food properly. Do they have food and water available at all times?
It's good that your keeping them warm, without the care and protection from their mothers, ducklings die very quickly if they get too cold and then develop a chill.
When you let them swim in the bath, make sure that they are dried off (gently) afterwards. And allow them to be in the water for not much longer than 10 - 20 minutes a day. And always make sure that they are supervised when in the water.
It's nice to hear you family loves them, they do make great pets and at times can be very entertaining. If you get anymore questions, just ask 
Mel X