For a long weekend, Florida sounds like an easy trip and a good choice.
For a long dive weekend I think you'd want to avoid any place that can be a bit complicated to reach, so as not to spend too much of your limited time on travel and to reduce the risk of delays.
Another spot to consider is the Cayman Brac Beach Resort. It's easy to fly directly from DCA to GCM and then a short half-hour hop over to CYB. It's all-inclusive with very good food, so you'll just have to concentrate on diving and getting the certifications done.
Right now Cayman Airways is offering $78 roundtrip fares from GCM to the sister islands, but I am not sure if you have to book their MIA to GCM special to get that price? That wouldn't work for you.
"Through-fares from the Sister Islands are available for an additional US$77.50 per roundtrip."
Wow! Cayman Airways Miami fares are now super low!
The CBBR resort is safe and clean and very similar to LCBR (CB is a bit nicer IMO, but I haven't seen the new renovations at LC yet) but CBBR has the same boats and dive op. So it's an easy "turnkey" trip to a lovely AI resort, with an excellent dive op, and very good diving. What's not to like?
CBBR were recently advertising specials for 7 nights, so ask what kind of deal they could give you for 3 people for a long weekend including 2 certifications. Call the booking agent directly, to see what's available, don't rely on their automated, online booking system.
Scuba Dive Packages at Cayman Brac Beach Resort
Wherever you decide to go, be sure that you make arrangements with the dive shop in advance regarding the certifications, to confirm that they will have staff available.
Happy Father's Day!