Ahoy, Joni!
Congratulations on booking your first cruise with Disney Cruise Line!
While both of these dolphin experiences offer incredible up-close-and-personal encounters with dolphins, you'll need to weigh your options regarding dolphin time vs. boat time.
Atlantis Dolphin Cay Shallow Water Interaction and Discover Atlantis begins with a a motor coach ride to the beautiful Atlantis Resort, followed by a 30 min. interaction with a dolphin. My family participated in this Port Adventure, and some of our favorite photos were taken with a dolphin with the Atlantis tower as the backdrop. So gorgeous! We felt like we had plenty of time in the water with the dolphins, and the trainers were fun and well-organized. After your time in Dolphin Cay, you're free to explore the resort, including "The Dig" and "Predator Lagoon".
The Blue Lagoon Island Dolphin Encounter provides a little less time with the dolphins, but includes a fun 40-minute catamaran cruise to the location. Once you reach Blue Lagoon Island, you'll get instruction from the trainers before a 15 min. interaction with the dolphins. After your interaction, you'll be able to enjoy Blue Lagoon Island before returning to the ship. If you book this Port Adventure, I encourage you to book an early time so you'll have plenty of time to enjoy the island.
Both adventures sound like a lot of fun. I've only personally experienced the Atlantis interaction, but would love to try the Blue Lagoon option. (That catamaran ride sure does sound like fun!) I encourage you to read both of the descriptions carefully and decide which one your family would most enjoy.
Hope this helps! - Diane