Guam for 10 days? And I heard people on this board saying they'd be bored in Singapore after three days...
Kids love wildlife --> Thailand? It is a short trip on the plane (12h to NZ can be a pain with a 3y old), you could fly to Chiang Mai, have the kids ride on an Elephant, do some nice (easy) hiking, then take one of their lovely night trains down to the south and spend some time on Ko Phi Phi or Krabi (If snorkeling and such meet your 'activity' requirements).
Other alternative - Bali? Lovely place as long as you stay away from Kuta (the local equivalent of Balneario 6 on Playa the Palma), plenty of wildlife (monkeys ), most lovely landscape, food and all kinds of outdoor activities. There is a tiny island named Nusa Lembongan southeast off Bali, no cars or roads there. I loved it. What might be a drawback is medical quality. In Thailand, you find European/US trained medical staff in any bigger city (and some expat doctors in most tourist centers). I don't know about Bali's medical standards, but I guess it matter when travelling with little kids. But most likely someone on Geobabies can advise here.
Kids are very welcome in both places, and the rather low costs of living mean you can always take the most comfortable option (which I expect would be budget-busting in Japan. But then, maybe not yours.
Bookmarked the thread. If I'm ever married, I'll send the link to my wife just after our ninth anniversary