The Bishop museum is the best place for your kids (and you) to learn more about Hawaii. Hawaiian Hall houses the largest collection of Hawaiian artifacts in the world, with many drawn from the Royal Collection. There's a hands on area for kids, and many of the artifacts will hold appeal for kids as well. Start here before your kids get too tired.
The highlight, for my kids was the museum's Science Adventure Center. The Centers focus on learning about Volcanos makes a lot of sense for Hawaii. You'll start your journey by traveling deep into the core of a (manmade) volcano, learning about lava, and then traveling up to the top of the volcano where you can peer inside the crater and see what an eruption really looks like. Once you've checked out the volcano, there's also a fun dress-up area, a hands on exhibit on windpower and air movement, and tons of information about local flora and fauna.