We travel from Detroit (about 1.5 hour shorter flying time than you) with our 2 boys every other summer. We've been doing this since then were 6 & 3 years old. Yep, imagine that looooooooooong flight with a 3 year old. Actually, it was fine, just realize when they are that young you will be the entertainment for 12+ hours and get a good night sleep before you go! But a 9 year old.......should be no problem. Our kids understand that it will be one solid day of travel, so they need to bring along enough for the plane to keep them.
I wouldn't make an overnight stop on the West Coast. We feel (and the kids feel) we would rather just suck it up for a long, full day of travelling and GET THERE and be done with it. By the time you would pick up your luggage, get to a hotel in LA or wherever and check in, get settled, etc. you could have been almost all the way to Hawaii! Any when you're juggling kids and their luggage.....too much hassle.
Typically
going from the Eastern U.S., you will leave in the morning and arrive in Hawaii in the afternoon (Hawaiian time) which will give you a chance to check in and then go for a swim, get some easy dinner (this is when room service or food by the pool is worth the $$$) and pass out in your beds.
Coming home, take an evening flight and sleep overnight and arrive home in the morning. On the ride home, we let the kids watch movies as late as they want (well, now that they're 12 & 9) on the plane. It's vacation after all!
As for what island......it depends what your family is looking for in a vacation. Oahu would make an excellent first stop. You can get off the plane there and check in without needing another interisland (which can be slightly confusing for your first trip, but not a big deal). Every kid (yes, even girls) should see Pearl Harbor. Try to rent some movies or documentaries or do some reading before hand so she understands the history of what she's seeing. Oahu has enough to keep you busy for a week......you can do "big city" things OR rural, isolated things.
Go to the library or bookstore and find the "Revealed" books by Andrew Doughty and Harriett Friedman of Wizard Publishing (Big Island Revealed, Maui Revealed, The Ultimate Kauai Guidebook.....
www.wizardpub.com) Then look through them and see what fits
your family.
We, as a family, love Kauai for its rural nature, excellent hiking, secluded beaches, etc. But I know it would be other peoples' hell on earth for the same reasons, plus its lack of shopping and non-focus on restaurants. But we're people that are more likely to grill some fresh fish or steaks at the condo grills than go out to eat. If your daughter likes to hook up with other kids to play with, she might not find the secluded beaches of Kauai that much fun.
My boys (9 & 12 this past summer) loved Maui for its beaches in the Waimea/Makena area, great boogie boarding in the summer, easy snorkelling from shore (Maui has way better coral than Kauai because it is a lot further south), and the chance to make friends at literally every beach with other kids. What we didn't like was the feeling that tourism had taken over much of the island and the crowds/traffic, long waits at restaurants, generally expensive dining. Hiking on Maui was not nearly as good as Kauai. Maui is also pretty dang windy!
Hawaii (the Big Island) is big.......plan to do a lot of driving if you want to see a good bit of it. We've been there because the boys had to see the volcano (being boys) and that was a total thrill because at the time we were able to walk right up to flowing lava (literally at our toes). But I'm not sure I would return there with kids because I hate to have them spend their vacation in the backseat of a car driving around. The other islands are much more compact and thus much more family-friendly.
But anyway, don't take me word for it,
READ UP! I would absolutely agree to just pick 2 islands and spend a week on each. You will be happy to truly get a feel for the islands, and you will be able to slip into "Aloha Time" and enjoy your family trip. Cruises really won't give you a true taste of any island, just a tourist view of ports. Don't waste your time and money.