Discovery Cove at Disney.
They have a mini water park that the dolphin encounter is park of. When we went a few years ago, they did not over sell the attraction, and it was a pleasant day all around. They do A?V talk about dolphins, get you suited up, and you do the encounter with a trainer. Only one group/family at a time in each pool, so it was very individual. My daughter loved it and says it was one of the best things we ever did as a family.
Some of my very good friends took their kids their to do it about 15 years ago. They enjoyed it very much.