My DH is also a diver (I'm not certified myself).
I can't speak for Sea World or for special excursion trips to the coast, but the only diving opportunity in the World is in the Living Seas at EPCOT.
Cost is $140 (does not include EPCOT admission) and you must use all of their equipment (you supply bathing suit, that's it). The program is a few hours long and includes about a 30-minute dive. The rest of the time is changing, orientation, etc. You get a certificate (I think), a stamp in your dive log, a T-shirt, and the opportunity to buy a video of the dive. They provide private lockers, showers, etc. and toiletries.
You must be PADI certified (and over 16) to participate. You must be fully certified, including completion of all of your open water dives and be able to present your card. My experience from making the reservation for him is that they are very strict about the certification (she emphasized several times that, without his PADI card, he would not be allowed to dive).
DH will be doing this for the first time on our upcoming trip and I'm very excited to have the opportunity to watch him in action!
Hope that helps.