Are you set on the South Pacific?
Because Turks/Caicos has most of the other stuff. Except maybe not "hundreds" of sharks but you will reliably see up to a dozen or so on just about every dive off French Cay or West Caicos - two sites served by boat dives from Providenciales (Provo) Probably no Tigers though. Jojo the Dolphin is a resident dolphin who regularly plays with people off the beach and we also heard but didn't see a pod off West Caicos. You won't find the diversity there that you will at some of your previous post locations - nothing in the Caribbean is that good.
What's nice about the T/C is there's a lot of deep walls which brings up the larger pelagics routinely and the corals are lush - coral on coral in many places you can't see the sand - except near the boat moorings placed there so they don't damage it. Some idea of what to expect - this is a liveaboard but you can access the exact same sites via dayboat from Provo.
Saudio's Trip Reports
Provo also has one of the nicest beaches in the world - Grace Bay Beach. It's 12 miles long so there's all sorts of accommodation options. It is a little pricey there though but you may save a lot on airfare - the Beaches is one of the more kid-friendly ones since you have some of those. For the family, it really is stunningly beautiful there.
Beautiful by Nature - Turks and Caicos Islands - Turks and Caicos Tourist Board
Stunning and Expensive - that's Wakatobi. How well do your kids travel though as it's a long way from North America.