Right, echoing the information that this isn't related to Hawaiian culture in any way, but as one of the founders of the Kona Chocolate Festival, now the Big island Chocolate Festival (March 21-23, http://www.konachocolatefestival.com/ ),
I do think that the whole process is fascinating.
Bob and Pam Cooper, the owners of the Original Hawaiian Chocolate Factory (the tour you're talking about) are transplants from the US Southeast who moved over here a few years ago and ended up with a farm with a few cacao trees on it. They decided to go for it with chocolate production, and have developed a really nice little agricultural operation on their land. It's not really a "factory tour" so much as a great insight into all that goes into making chocolate - very few people have any idea of the process.
Chocolate/cacao is slowing gaining ground as an agricultural commodity in Hawaii.
Your plan to use your trip as a cultural educational experience for your children is a wonderful one. One of the best ways to begin is to start doing some pre-trip research with them, so that when they arrive they have some basis of understanding what they will experience here. I can provide some resource links for you if you're interested.
Then, when you are here, one the easiest ways for them to start absorbing the culture is to visit some of the significant cultural sites that are set up for relaxed, self-guided interpretive tours. Tops on the list would be:
Pu'ukohola Heaiu, in Kohala
Pu'uhonua O Honaunau, in South Kona
Lapakahi State Historical Park
There are many other culturally significant sites you can visit all over the island, but unless you go with someone who can explain the sites to you, it's difficult to really understand them or to use them as a teaching tool for children.
There are also many opportunities at Volcanoes National Park. Many of the sites there have some cultural information on interpretive signs (and they are adding more), and even better if you can connect with some of the Native Hawaiian park rangers there, who give very special tours focusing on one or specific cultural aspects.
As for other kinds of activities, there a few different ways to get them out in a traditional Hawaiian outrigger canoe. Outrigger canoes are an iconic part of the culture throughout the Pacific Islands - Polynesians, skilled seamen that have had no equal before or since, traveled across vast expanses of ocean on voyages to distant locations, relying on celestial navigation and close observation of currents, winds, seabirds, schools of fish, and a "virtual map" that was held in the mind.
Some of the ways you can do this are:
Kona Boys (at Kamakahonu Beach in Kailua-Kona)
(not so much the double-hull tour to Kealakekua Bay, as that one has a motor and so is not traditional - instead, go on the 6-man wa'a)
The double-hull sailing canoe with Kiko Johnson
(one of Hawaii's best watermen - he shares a LOT of cultural information on his tours)
The Kinikini sailing canoe out of Keauhou Bay
Also, the Imiloa Astronomy Center in Hilo has a wonderful exhibit about the canoe in Polynesian Culture - highly recommended!
Also, if you are visiting during the months of late May - late July. there are outrigger canoe regattas every Saturday. The race venues rotate back and forth between the Kailua-Kona Pier and Hilo Bay, and this is a great opportunity to see the beautifully handcrafted koa canoes (worth about $100,000 each) up close, and racing - early in the day your kids can watch kids their own age racing in these amazing canoes! You can download the 2013 race schedule here (crazy long link, sorry):
Hula is, of course, a major cultural activity. Almost monthly, there is a hula kahiko (the style of hula before Western contact) performance at the hula platform at VNP, and many of the kumu hula share a lot of cultural information as part of the performance. On those days, there are also hands-on cultural workshops at the Volcano Art Center front porch. You can check the schedule of these events here:
If you're interested in going very deep into your family's understanding of the culture, and what it means to be living the culture in the 21st Century, check out the site for Ka Welina Network:
This is an alliance of ten Kanaka Maoli (native Hawaiian communities) that welcome visitors to come and learn more about them and what they do. These are NOT tours, and you must be invited to visit, and because these communities/organizations are primarily cultural practitioners, a visit can only be arranged if your schedule meshes with a time that they are able to host visitors. But if you can make these arrangements, you will gain an understanding of the culture that very, very few visitors ever do. Just reading the materials on the website will be extremely informative.
Again, mahalo nui loa for your interest in providing an education for your children as a key element of your trip! I hope you have a very rewarding visit.