Can you tell me what my family and I should not miss out on while visiting Hawaii on our summer vacation?

Some of the activities you mention, like the fire dance, is not Hawaiian, but often included at a luau show. I would make 3 suggestions as must do's so you can experience most of what's on your interest list.

First, go to the Polynesian Cultural Center. Its located on the far northern end of Oahu, about an hour's drive from Waikiki, but you can experience several Polynesian activities listed on your list in one location, and in a pretty authentic presentation. They have a dinner show, "Ha: Breath of LIfe" that is pretty good as well. Oh, PCC does not serve alcoholic beverages, if that's a deal breaker for you...it is operated by the Mormon Church. http://www.polynesia.com/

Optionally, you could skip the luau/dinner show at the PCC and attend one of the many commercial luaus offered elsewhere. I would suggest either Germaine's or Paradise Cove. You can look all 3 of them up online and compare menu's and prices. http://www.myhawaiifoodfun.com/myhawaiionline-blog...

The 3rd stop, located about 2-3 miles from Waikiki (depends on where you're staying) is Helena's Foods. They are not the only Hawaiian food restaurant, but one of the more accessible from Waikiki and admittedly, one of my favorites. There you can get your kalua pig, laulau, haupia, poi, lomilomi salmon, and other Hawaiian foods. http://helenashawaiianfood.com/

Bear in mind, its a small place and as tourists, you will stand out! You can also get many of these foods at the Ala Moana Shopping Center food court, located on the lower level, ocean side, near the center. Worth checking out...about 20 minutes from Waikiki.

I should also mention that the #1 tourist attraction in number of visitors is the Arizona Memorial, although there's a lot more to see at Pearl Harbor than just that. http://www.myhawaiifoodfun.com/myhawaiionline-blog...

Enjoy the whole Island. How i wish i can go there. may you & your family have a good time.