Hi - I have traveled in Croatia and Slovenia several times (4), have used Rick Steve’s Book like a treasured friend each time. I am of your family’s age, so I can relate well to their interests ( museums, adventure and food)..
First, be aware that flying into the Capital is different than flying out of Dubrovnik - all transportation here must be well planned: car rental and return, limited use of bus, very few train lines, excellent toll roads and ask rental car company how to use them, strict ferry schedules ( and know the difference between fast Cat and the car carrying ferry.)
You can plan to either have your trip begin and end from the same location or do a logical one direction trip ie north to south seems to be your preference. Personally, I would rent car in Zagreb and drop it at the Split airport after leaving luggage and a few travelers in Split, returning to accommodation by taxi. I would then travel on the Fast Catamaran through the islands to Dubrovnik. I would taxi to Dubrovnik gate and find accommodations inside of the old city.
To return to Split I would hire a driver, take the coastal road, make stops along the way to spend 1 night in Split and fly out of Split! The car will not be as important as you might think on the islands.
The capital is a large city- interesting and I’m sure some people could stay a week, but you dont really have much time and want to see quite a few things.
Straight to Rovinj, stay in old town, spend the money to park your car close for day trips:
I found a nice place on the water with two bedrooms (4 people) for a reasonable price. Restaurants galore, saw a Miro exhibition there in a small art musings - Rovinj has a charm that is unsurpassed and at one time was Ricks favorite town. I adore old town.
Day trips include (1) the hill towns (most see Motovun, I’ve walked the walled pathway (nice) but I have stayed in the small artist town in Groznjan ( lovely);
(2) south to Pula, the 6th most complete Roman Amphetheater in the World; Tito’s home the island of Brijuni; (3) Drive to the Lakes maybe a 5 hour drive, but longer on coast to see Opatija (nice), spend at least one night near P.Park. Your plan is good, but don’t take the wrong walk like I did and made my 90 year old husband exhausted - be sure to go in the direction that will be mostly downhill; Skip Other K.Park (4) Drive to Zadar it has historic old town, pick accommodation carefully. There is one of the nicest small Archeology Museums I have seen - worth the stop! (5) Split at least 2 full days, do not miss the famous sculpture’s US citizen who did the Two Indians on the ends of Bridge in Chicago and La Pieta at U Notre Dame South Bend : Ivan Mestrovic Gallery; return the car - there imay be return offic for your car in Split too. (6) Begin journey by fast Cat: 1 night in Bol, a couple in Hvar, a few more in Korcula ( which I like best) - remember the sword dance Thursday night, then off to Dubrovnik to stay inside the walls... I stay close to the upper gate. (7) Return to Split by hire car/van along coast to spend last night in Split - Fly out the next day. I loosely counted days and came up with about 16... it is a great trip and I don’t know your flexibility in length. Enjoy Croatia it is wonderful!
Four trips, longest 1 month. Susan