Key Largo is certainly an option because if the WX is knarly, you can still have fun enjoying the upper Keyes lifestyle. But, keep in mind that there are no shore dives in Key Largo.
Expect travel from Orlando to be about 4.5 or more hours depending upon Orlando traffic, fuel, food, rest, speed, en-route traffic/accidents and time of day/weather (WX).
As far as holiday's; the traffic in the upper Keyes (Key Largo) can be VERY, very, slow around (before and at the end of) three day weekends. But to be more specific to your question; on driving in/out Saturday and Sunday: EXPECT a parking lot during the holidays and at minimum, much heavier traffic on the weekend than during the week.
In response to your question on how often the boats go out down here ....I use my own boat so I cant say for sure (suggest you make some phone calls to the dive boat Op's) but I see dive boats going out here in Pompano - Ft Lauderdale 7 days per week in a lot of interesting WX conditions.
Bvarn1 gives good advice about Pompano, but again provided WX is good.
And here's a link for you on a shore dive down here:
Florida's Best Shore Dive - Go Dive Florida
Hope this helps.