A range of things to think about. Some thoughts:
In general with kids: sand beach, a good kids' club, access to casual diving like a buffet is nice, and destinations more likely to have 'first world' health care in case a kid gets sick are nice. The kind of non-diving excursions you find in popular cruise ship ports are also nice. My first dive trip with a baby in tow was to Key Largo, with access to U.S. hospitals in my mind. Budget-friendly is good when hauling that many people and you've got a family to support. Long plane rides and little kids...ugh!
1.) A Cozumel A.I. with a sandy beach and a kids' club was my first thought. With kids, a sandy beach sloping into the ocean is great. A kid's club the kids love that gets them out of the grown up's hair is also great. Casual dining options like a buffet are also good news. San Miguel is a neat place to walk around. As a cruise ship port, Cozumel has non-diving excursion options, including dolphin encounters (which can be magical your first time).
Be mindful it's drift diving, that's not always the easiest for the macro. you mentioned, and not all sites are shallow.
2.) You might consider an A.I. resort in the Dominican Republic. It doesn't get as much attention as Cozumel, but I hear some good things. On a cruise ship in Samana (not where I'd stay if diving), did an ATV ride - nice people, good time.
3.) Bonaire - the little sandy beach at Den Laman/Sand Dollar is pretty small, and the Den Laman side was rockier when I was there. I love Bonaire, but not what I'd pick.
4.) Curacao - I didn't try the shore diving. Family enjoyed Sunscapes Resort Curacao; the total trip bill was pricey, but our daughter loved the kids' club. The nearby Sea Aquarium has dolphins, and while it's no Sea World, it's a nice place to visit and your kids could enjoy an afternoon there. If you do an ATV tour and they offer to sell you a bandana, TAKE IT!!! Best $5 you will ever spend (cheaper than a new set of lungs).
5.) Caymans - with your group I'd do Grand Cayman for topside amenities for the non-divers, and probably cough up the cash to stay along 7 Mile Beach (but I'd be checking Comfort Suites or Sunshine Suites Resort, IIRC, as the more budget options in that area). Grand Cayman's a cruise port, so there are well-developed excursion options - including dolphins. But I don't read of A.I. resorts, and in resorts that aren't as expensive, what about kids' club options? Don't know about that...
6.) The long round trip boat rides I read of with Turks & Caicos (really Provo.; Grand Turk is a different practical situation) and the expensive topside (on par or higher than Grand Cayman by rep.), but not being a big cruise ship port so maybe not so many topside excursion options... The diving is often deep. I enjoyed T&C, but liked the reef better diving the Caymans, and I doubt this is your best option.
7.) Never been to Hawaii. I'm told the water is chillier than the Caribbean. Endemic species are a draw; I'm under the impression lush reef not so much? Again, haven't been there. The Kona night dive with mantas sounds great. If you're going to take them to Hawaii, I suggest waiting till they're older and better remember the trip for the long haul...maybe when the youngest is 8+? It's such a 'brand name,' expensive, long flight place...who wants to say when went there at age 3 and don't remember it?
Note: My OCD brain goes on the fritz just thinking about researching the options of a Hawaii trip with all those weird place names.
8.) St. Croix could work. Minor cruise action, a little 'sleepy,' but you can find a range of things to do, there is good beach and it's a neat place. We enjoyed a Tan Tan Tours jeep ride - but if you're addicted to the idea of seat belts and car seats for your kids, you might not. Total trip cost can be a bit pricey; I don't hear of many A.I.s.
9.) Chilly mentioned Ambergris Caye, Belize, and it's what I thought of. I've only dove Belize via live-aboard. It's my understanding A.C. would give them sandy beach and ocean fun, while keeping you close to the mainland. I don't know about topside resorts and kids' clubs there. On a cruise stop years ago, we took a boat excursion up New River to Lamani ('submerged crocodile'), walked in the rainforest, visited 3 (climbed atop 2) Mayan ruins (Mask, Tall and Jaguar Temples) - this was pre-kid - and even saw some crocodiles on the river. Nice! If you care to spend a few non-diving days on the mainland, Belize has some things to do. Since cruise ships hit the mainland, on A.C. you may not have immediate access to lots of excursions?
So, to narrow it down before it drove me nuts, I'd take these options (Grand Cayman - Sunshine Suites or Comfort Inn), Cozumel (A.I.), and Dominican Republic (A.I.); be mindful Grand Cayman (from what I've read) doesn't seem to be a big 'A.I. place,' and has a rep. for being pricy. Factor food costs in when you compare trip costs. If the budget allows, consider Sunscape Resort Curacao.
If money's at all tight, I suspect a Coz. A.I. or Dominican Republic A.I. is your friend. Coz. gets far more attention and compare excursion options (e.g.: has D.R. got dolphin encounters?)...whether you like drift diving is a big deal.
That's just my thinking, and I haven't been as many places as a lot of people.