Welcome aboard, Debbie!
My daughter and I participated in the
Blue Lagoon Dolphin Swim a couple months back and it was such a great experience! I see that your son is nine, so as long as your daughter is six or older, you're all set. The swim is so much more interactive than the dolphin encounter there, so in my opinion, it was definitely worth the extra cost. This was a special experience for us, and my daughter was as happy as I've ever seen her as she was able to pet and hug the two dolphins that were with our group. Also, we were in a small group of only four, while the folks on the encounter had many more in their group. So, two dolphins, four people, and a long fun time interacting with them and being pushed across the water - so amazing! It varies by group though.
Lunch was not included in this because guests had the option to head back to the ship on the next shuttle boat after our swim, so not everyone stayed on the island for lunch, but food is available to purchase.
If budget-wise, you're only looking for a beach day, I'd say skip the beach in Nassau altogether and just spend your beach day on Castaway Cay when you port there. You won't find a better beach than that, plus everything there is included! But, if your budget allows, this particular dolphin swim was certainly a very special experience for us, and we did enjoy exploring Blue Lagoon Beach afterwards too. Another option is for two of you to swim and the other two to join the
Dolphin Observer, going along with you, but simply watching from the dock above instead of being in the water.
I hope that helps as you plan, Debbie!