Letiole gave you a very accurate assessment of the resort. Generally speaking, you'll find more mosquitoes wherever there are more trees and rainfall (e.g., the windward side of the islands). The Moloka'i resort is on the leeward (western) side, so it doesn't get as much rain.

If you've already been to Maui and O'ahu, and want to see another Hawaiian island, you might also want to consider Kaua'i. It is the norternmost of the main islands, and it gets a fair bit of rain in the winter, but, IME, has the least problem with mosquitoes (despite the fact that it's really really green). It's a lovely island, and the Sheraton in Po'ipu is definitely a kid-friendly place. There's a lot more to do and see on Kaua'i than on Moloka'i for someone who hasn't been to Hawai'i too many times already.