"My uncle and my father were drinking orange juice that day."
Translation:Mi tío y mi padre bebían jugo de naranja ese día.
There is a subtle difference. I believe using "estuvieron bebiendo" would mean they drank orange juice for a limited or defined account of time on that day (say during lunch). Using "estaban bebiendo" or "bebián" would mean they drank orange juice throughout the entire day (any time they were thirsty they drank orange juice).