We've stayed at the BC for a few years during Easter. Usually they have a candy scatter on Easter morning around 9 a.m. They roped off a few different areas and spread candy and plastic eggs inside for the kids to gather up when the whistle blew to start. The roped off areas were separated by age groups to keep things fair. They'd also have some crafts set up in the same area, and the Easter Bunny usually made an appearance. I believe there would be Easter-type activities going on at the pool all day too. I don't remember long lines anywhere except maybe to see the Easter Bunny.
As a side note, we'd then go into Epcot for the day and traditionally it has always been a great park to be at on Easter Sunday. We don't find it to be crowded at all. They have a few fun areas set up for the kids where they can find plastic eggs with little trinkets inside.