I agree with vincent.
I'm almost positive the Tarpon Cave at Turtle Reef is above 40'. In some places the bottom of the mini-wall to the south is about that - or less than 10' deeper. And it bottoms out into sand so no reason to do that anyway typically. I'm pretty sure our second dive there we never broke 40'. And it's a good dive, the mini-wall is covered in stuff. Happy Fish Divers does guided dives there also - they work with Sundivers on-site.
At Lighthouse Point the reef starts in 6' off the dock. Cobalt Coast is pretty similar.
Sunset House has decent reef structure above 40'. Time the sub passing and the kids can wave to the tourists. (ask at the shop) The mermaid is actually 55' to the base but they could get pretty close - it would just be blue water diving for them though as there's not a lot shallower in that area - she's kind of in shallow fold in the reef.
Parts of Eden Rock are 15' deep. Once you get out to where the reef becomes patchy (don't go further, it won't get any better) you're at about 42-45'. But there's a lot of reef in 20-30' also. Some of the swim-thru's at the Grotto nearby are pretty shallow also - don't remember the exact depth. Cheeseburger Reef in town off Lobster Pot Dive is similar. If possible you'd want to dive them when there's no cruise traffic since they're within 1/4 mi. of the port or less. We had Eden Rock to ourselves after 4PM one afternoon. They close at 5 so rent a 2nd tank on a 24hr. rental if you want to dive there twice.
Stingray City is the most fun they'll have in 14' of water. There's also Cemetery Reef north of Seven Mile Beach but it's really a better snorkel than dive. And Smith's Cove south of Sunset House. Rent tanks at Eden Rock for these - most other ops don't let you remove them.
They could also dive the Kittiwake IIRC. All that's required is an OW card to access the top 2-3 levels of the ship. It was put down as a combo dive/snorkel site so it almost breaks the surface. Diver cleaned so it's safe and the rules require a DM per group/level - AOW and wreck cert divers can penetrate deeper.
http://www.dive365cayman.com/kittiwake-cayman
There's also a lot of boat dives that are within the kids range. Talk to Jason at Ambassador Divers - they'll go with 2 divers - 6-8 max, so he might be able to do some "private" charters for the 4 of you at their regular 2 dive rate.
Dive Sites lists about 30-40 dives above 40'. If you've got more divers with you - with 6 pax you'd "own" the boat at many of the operators. Here's the big list:
Cayman Islands Tourism Association - Things To Do In Cayman, Cayman Culture,Cayman Islands Watersports
I'm sure we weren't much more than 40' at the Aquarium and that was only because we followed one of the sand chutes down the wall. Many of the cleaning stations are above 40'. The cleaner shrimp will trim cuticles if you hold out your hand. Another 2nd dive nearby - Mitch Miller is at 30'. The topography there is different than nearby which is why to dive it.
http://www.dive365cayman.com/dive-sites for many more - they list depths.
Red Sail does a single tank afternoon shallow dive guaranteed to be between 30-50' max.
One Tank PM West Shallow Dive | Cayman Islands | Red Sail Sports Cayman
We could always return to Bonaire but would like to let the kids experience a different island.
fyi, Bonaire with a lot more to do on the surface - and much easier shore entries - is called Curacao. We did 25 dives there - only one from a boat to get to a site not shore-accessible.