My wife and I did the dolphin dive through Anthony's Key back in 2005. Couldn't recommend it with any greater enthusiasm! You are introduced to the dolphins at the dock behind the research center. They are free to come and go as they please but they are trained to allow inspection and you actually sit with one on your lap. The operators take the dive group out a small distance and you dive to about 60 ft. to kneel on a sandy bottom. The dolphin zip around and play and the trainer tries to keep them out of his pocket… where the treats are stashed. It looks like a pet trying to get the trainer to release some goodies.
They glide and swim just inches away from you. Just when I thought our dolphin was going to slice my head off with a pectoral fin, the dolphin retracted it and cleared my mask so closely that I instinctively yanked my head backward to get out of the way. They say not to touch them but that’s a hard, hard choice to make when they are so affectionate. However, I didn’t see anybody corrected for touching. BTW, one of the pair that were supposed to accompany us decided he didn’t want to play so he left unexpectedly (was it something I said?) while the party remained until each diver had about 700 lbs, then you were sent up to your safety stop. So my wife got to spend significantly more time with the dolphin than was I. I’ve been working on my breathing ever since.
We have not dived Cozumel and only did our very first “Discover Scuba” dive with Bob Soto’s Reef Divers in Georgetown, Grand Cayman in 2003. Unfortunately, the dive could easily have put a quick end to our diving together as the young divemaster was just trying to get through her day and used uncommon means to complete the dive with the rest of the group while my wife had clearing and buoyancy problems. She ignored the signals my wife gave her and apparently did not know how to correct the situation. The subsequent yo-yoing and changes in pressure ruptured my wife’s ear drum which we did not notice until while heading back to the cruise ship, I spotted blood coming from her ear.
Of course the good part of the story is that my wife came back from that to become a Master Diver.
Good luck.