I've dove at many of the places people mentioned myself.
Epcot at Disney was a blast. It's not cheap though. If you dive there, buy the video. It's excellent and the kids will treasure that. They can show their friends with pride, of what they can do at Disney. Other non-diving family members can watch in delight from outside the aquarium.
The Crystal River, King's Bay cave, was ok. Dove both during day and night. The nearby Rainbow River is a very nice shallow drift dive. Excellent Viz. It's easy and excellent for beginners (and experienced). Others can snorkel or just stay on the pontoon boat with nice topside scenery.
Key Largo also has many excellent reef locations. Also several dive op right by the hotels there. We've stayed at the Marriott (even when it was Ramada), right by Rainbow Reef dive shop. Rainbow provides a free dive guide if you ask for one, and give multi-dive discounts. Capt. Slates has the Creature Dive, where you can see huge Goliath Groupers, and eels.
All will give your kids great in water experience.