Vis, Korcula, Omis, Biokovo Mountain

Zagreb--sounds good
Plitvice--many recommend just a night--an afternoon/evening hike and then one early the next morning should suffice, but for avid hikers there are some other trails in the area.
Split--okay

I would not go to Vis unless you can give it at least three nights for two full days. It may not be warm enough for swimming (depends on where you are from and your tolerance for cold water), so that might give the mainland the edge. You would be limited to car ferry schedule if you take the car, but you definitely need wheels on the islands (we used scooters, there are car rentals on the island as well).
Korcula might give you enough proximity to the mainland--check drive times to see what you could combine. Definitely only two stops over five days would be my recommendation.

You could probably just stop at Trsteno en route, but that is a good option for daytime when cruisers descend.

Thanks so much for the input. We have time to fit in 3 nights in Vis... do you think Vis is worth it/better than 3 nights in Korcula and 1 day in Makarska/Biokovo Mountain?

If it was swimming season, the beaches of Vis are some of my favorite in Croatia, but I think in mid May, the sea will be so cold that maybe hiking on the mainland would be more enjoyable.

We visited Croatia, Montenegro, and Ljubljana last September. We are probably older than you and your family, so we weren't interested in ziplines or ATV tours (I was recovering from hip replacement surgery) so I can't comment on those, but I will try to give advice based on our trip.

We loved both Zagreb and Ljubljana but they are also very different cities architecturally and visually, and the food is very different. Ljubljana is very pretty with a river running through it, some very pretty bridges, and cafes and restaurants lining the river. It looks very different from Zagreb. Zagreb reminded us of a smaller version of Prague, similar architecture, ambiance and food. The Old Town has 2 levels; there is a wonderful, large outdoor market, and lots of small and unique museums. If you rent the car in Zagreb, then you won't have a large drop-off fee. If you fly into Ljubljana, and rent your car there, then you will have a huge drop off fee to return the car in Dubrovnik. Or you could take the train from Ljubljana to Zagreb, and pick up the car there. But it would be a shame not to spend any time in Zagreb if you are already there picking up the car.

Plitvice Lakes National Park - You have a good plan! That's exactly what we did!

We spent 4 nights in Split and loved it! If you have the time, consider hiring Maja Benzon, recommended by Rick, for a private guided tour of Old Town and Diocletian's Palace. We took the catamaran for a day to Hvar Town on Hvar Island. It's the only island we visited so I can't give advice on Vis or Korcula. We loved Hvar Town! It is beautiful! So perhaps you could spend 2 nights on Hvar and 2 or 3 nights on Korcula? (For those middle 4-5 days you asking about.) Or hiking on the mainland as valadelphia suggests.

You need 3 nights in Dubrovnik to do what you are thinking of doing, although I don't know if that is enough for a half day trip to Trsteno. Depends on when you arrive in Dubrovnik. We spent 3 nights in Dubrovnik (which we loved, BTW). The crowds did not take away from our enjoyment of Dubrovnik and its beauty. We hired a private driver for a day trip around the Bay of Kotor. And we had one full day in Dubrovnik. There is more to Dubrovnik than just "walking the walls", which is amazing. I think all visitors should visit the War Photo Limited exhibit. This is a permanent exhibit on the war in the former Yugoslavia in the 1990's. It helped us understand the complex war a little bit better. Very sobering and tragic. And there was a temporary exhibit on the Vietnam War. I believe this temporary exhibit changes every year. We also visited the Franciscan Monastery, and took the cable car to the top of Mt. Srd for spectacular views of Dubrovnik and the Adriatic, and had drinks at the Panorama Café.