Croatia for 1 week with 5 adults and 6 teenagers

With one week I would visit Split (2 nights), ferry to an island, probably Hvar (3 nights) since you have teenagers, then ferry to Dubrovnik (2 nights).

In Split they have blue caves for snorkeling, or a visit to Krka national park. Hvar has hiking and swimming. In Dubrovnik you can hike up or down or both to Mt. Srd, you can ferry over to Lokrum Island and hike/swim have lunch at their only cafe, Johnny is the owner, or go kayaking. Also walk the walls which is an urban hike in my opinion.

What Barbara said. Though I might say 2-2-3, just because Dubrovnik is such a hive of activity and options. With such a large group, everyone could easily cut loose and do their own thing there.

I would definitely recommend an all day boat trip to the Blue Caves and Bisevo (we went out of Hvar, also available from Split). That was a highlight of our trip, I will never forget swimming in secret caves and jumping off the boat, there were even cliffs to jump from.

I like Split, but in your case, I'd split after a night at most--just time to see the basics. Spend four nights on one island (any of them would be great) and then the remainder in Dubrovnik. Or, if you were feeling jazzed about Split and want to take multiple day trips, split the time between Split and Dubrovnik, but I think an outdoorsy group would like being on an island for the variety of activities (some can sit on the beach or tour villages, some can go kayaking or windsurfing, some can hike, etc.)
On Hvar, you might tour the lavender fields, take boat trips to Pakleni islands.
Brac has a cool monastery to tour and windsurfing.
Vis is nice for renting scooters (being much smaller) and hiking to secluded coves.
Korcula has vineyards.
All of these islands are equally appealing and there is overlap among the generalizations above. I think with limited time, the key is to pick one place and not run around too much.