Some people spend a full day at Discovery Cove while others get there, swim with the Dolphins as soon as they can, and then leave. So you can make it a full day or a short day. Even with something else planned at 6:30, you should be able to spend most of the day there and not feel too rushed.
The big thing at DC is, of course, the Dolphins. The entire experience, from the information session to the purchasing of pictures, probably takes a little over an hour. The rest of the day is entirely at whatever pace you want to go.
There really aren't a lot of things to do there. Besides the Dolphin swim, there is snorkling around the coral reef, wading with stingrays, the lazy river, lounging on the beach, walking through the aviary and lunch. So you will have plenty of time to do everything without having to rush through any one thing.
Due to an unfortunate illness which led to a last minute rescheduling, our visit to DC was on the last day of our vacation. My friends had to be at the airport by 3 o'clock so we could not stay the entire day. Even with the shortened day, we ended up doing everything except for the aviary and we did not feel rushed at all.
So as long as you get there fairly early, you should be able to have a relaxing time and still make the Backyard BBQ.