I was going to suggest an island resort too....no car hire or travel, so no worries about car seats etc. Self-catering accommodation but there's takeaways and restaurants if you like. Some resorts are all inclusive.

My brother swears by Hamilton Island too, though not sure how kid-friendly it is (they didn't have kids last time they went). He said wildlife (birds, not sure what else) came right up to the house they rented and there was a zoo there too...

Not sure how $$ a week in Fiji or Vanuatu is now.... we stayed in Fiji on Denarau Island about 7 years ago now and there were heaps of free activities each day (pool, beach games, coconut dehusking, dancing to watch, basket weaving and traditional crafts etc), you could easily fill in a week without needing to do organised tours. Meals were included, there was a free bus around the island and the bus/taxi into Nadi was 50 cents! There's also a kids club.