Two weeks will give you the chance to visit and experience two of the Hawaiian islands quite well. Which two you choose is up to you. Maui and Kauai are both beautiful places, but I'd also suggest you consider the Big Island as one of your destinations. In fact, if you've never been to Hawaii, I'd suggest you go to the Big Island, then finish in Maui. These are my two favorite islands, not to say the others don't have their charm as well.
I'd say you need to decide how active or sedentary you want your vacation to be. If you want a busy active vacation, I'd pick the Big Island over Kauai, and add Maui to the itinerary. The Big Island has Volcanoes National Park, an absolutely fascinating place that you should spend at least one and maybe 2 days at. Hilo and environs is worth another day, and the rest of your time can be focus around Kona and the northwest part of the island. So ideally if you are on the Big Island for a week, 2 nights in Hilo are good for access to Volcanoes N.P., plus 5 nights in Kona. My blog has lots of details on what to see and do in the Big Island, so I don't want to go through it all here again, but if you want to read and see more about it, please click on this link:blog/category/aall/north-america/hawaii/">http://drfumblefinger.com/wrdprs/blog/category/aall/north-america/hawaii/
Maui is the best island for snorkeling and has some of the nicest beaches, plus Haleakala is a great day trip as is the road to Hana. Very popular places to stay in Maui are West Maui, and to a lesser extent South Maui. Both of these places are in the rainshadow of the island's old volcanoes so they are relatively dry. You'll find most rentals here. More info on Maui can be found at the above link as well.
You certainly can fly into one island, catch a shuttle flight to another, then return home from that second island. For example,, you can fly to Kona, fly Kona to Maui and return home from Maui. I think most airlines won't charge you a penalty for this but check out the major flight engines like Kayak.com or Expedia.com and try this on their multiple destination flight option. See how this prices out for the four of you. Fortunately flights to Hawaii are much cheaper in the summer than in the winter.
And with 2 teenagers a condo rental makes lots of sense. The extra space is very appreciated when you're together in close quarters for a long time, and it gives you the opportunity to make a few simple meals for the cost of groceries (eg. cereal for breakfast, sandwiches to take on the road). Food is expensive in Hawaii, and eating out 3 times day day will take a lot of time and eat into your travel budget. Homeaway.com and VRBO.com are two good search engines with lots of condo options.
Good luck with your plans! Hawaii is great -- there really is no wrong place to go there.