There's more to do on Maui, but Kauai is our favorite island - easier to get around and prettier
Maui - The west side is very nice, as is the Wailea-Makena area. Don't be lured by the prices in the Kihei area. The Road to Hana can be done in a private or semi-private van tour, which is easier on whoever would be driving the rental car. The volcano is pretty much a must, but I didn't think sunrise was worth getting up that early, given the crowd on top. A snorkel tour of Molokini and turtle town would be high on my list of things to do with kids.
Kauai - The surf is large in the south of the island during summer, so I'd be prone to stay in the north or maybe the Marriott resort in Lihue if you spring for a room with a view or one of their timeshare condos (1br, 2 ba). The Marriott is centrally located, has a terrific pool with 5 hot tubs, gentle surf beach, and Duke's restaurant on site. Do not stay in the Kappa area. A drive up Waimea Canyon (with a stop at Spouting Horn on the way), a Na Pali coast boat tour (especially one that takes you to The Forbidden Island), visiting the lighthouse (with a stop at the Hanalei Valley lookout for a family photo) and a drive through the eucalyptus tree tunnel (with a stop at Koloa Mill Ice Cream and Coffee afterwards) would be on my list of things to do. Your kids would enjoy the glass beach near Port Allen. Maybe Wailua Falls or Fern Grotto, but I haven't done either. Check to see if the Bali Hai restaurant has reopened. If so, book a reservation for sunset and apologize to your kids as they might be bored - your wife won't as the views are unbelievable.
Wherever you go, I'd skip all luau's (expensive and will bore your kids to death) and never, ever eat any poi. Arrange for a lei greeting upon landing for your wife and any daughters. Skip the resort gift shops and stop at a Hilo Hattie's for all gifts/trinkets. If you plan on doing much snorkeling, are visiting both islands and don't bring your own equipment, use a place where you can rent on one and return at another like Snorkel Bob's. They also rent RX masks.