At Dolphins in Depth you will learn a lot about dolphins and you do have about 1/2 hour interaction with them in the water. You do not actually swim with them, though.
Each experience is limited to 8 people max, so it's a good idea to make your reservation as soon as possible.
You will be required to put on a wetsuit and water shoes to go into the water. You stand on a ledge at the top of Living Seas with 2 of the trainers. They bring the dolphins over ... but it is always up to the dolphins to choose whether or not to interact. (The best days to go are early in the week.)
You do get the opportunity to give both dolphins a "massage" of sorts -- a rub-down on their sides. The trainers divide you into 2 groups of 4. First, you have your picture taken with your arm around either Calvin or Rainier. Then after doing some tricks, you stand in a line and rub their sides lightly for a few minutes. The trainers instruct you on how to do this -- no grabbing, poking, kneading, etc -- just a light left to right rub with your open palm. Then the groups switch dolphins and you repeat the process with the other one! (They feel like wet rubber.)
The tour costs $140 per person, and that money goes to the Disney Conservation Fund. The tour is fantastic and you will both have a great time.