13 day Itinery starting mid June

Concerning Rovinj vs Pula. Do you want to just chill and relax on the beach, go to Rovnj. If you want history head to Pula. The beaches are harder to get to and not as nice in my opinion. From Zadar you could go by ferry to Šibenik (underrated city) then ferry to Split, pick up car and drive to Mostar then drive to Dubrovnik dropping off car. Any of these places one night would be sufficient but I avoid one night stops unless they are absolutely necessary. The ferries are a great way to get up and down the coast. Buses are too confining and too slow. Check out croatiaferries.com for timetables. Always try to book on the catamarans (Krilo) as opposed to “the ferry” which would be Jadrolinija. The ferries take cars, pets, bikes, etc. and take much longer. Krilo runs fast catamarans. So if the description says no cars, etc. You’re good to go. Zadar was our only one night stay, but we were there to visit an elderly cousin for dinner so we really didn’t sightsee this trip. The Sea organ plays music all day (you can’t see it) and the Greeting to the Sun light show can take you 5 minutes or 5 hours, depends on you. There is an old park in Zadar which is a lovely place to take a walk and enjoy nature.
In Split we always stay at the Hotel Peristal which is inside Diocletion’s palace. Quick walk anywhere, great location. Lovely people, breakfast included. They also have an outside restaurant where we would have an afternoon drink.
Trogir is an easy bus ride, or ferry from Split. A very short walk from the hotel. About Korcula. We love it, but we have family there so we always go for a few days. It is a beautiful island with a long history. It is a ferry ride from either Split or Dubrovnik or the other way. But if you are short on time, it is very similar to Dubrovnik. If I had to cut one place out, it would be Korčula because of this and it is the furthest out.

I just reread your post. Are you flying out of Split or Dubrovnik to italy? If split, just reverse the order.

Warning: I haven't driven anywhere in Europe, much less in Croatia--though I have been to the country three times.

I assume you mean you're going to pick up the car before leaving Zagreb. It will be extremely helpful to have a car to get to Plitvice and around Istria. Both are manageable by public transportation, but that takes more time than you have.

Fiddle around with driving routes and estimated driving times on ViaMichelin.com. I think you will do better if you change your route to Zagreb-Rovinj-Plitvice Lakes-Zadar etc.

If you can get to Plitvice by about 2 PM, you can probably accomplish a lot in the park that afternoon as the day-trippers begin to leave. You'll have very long daylight hours in June; just take some snacks and water with you so you don't need to leave the park earlier than you want to. I found the estimated times for the marked routes to be overly generous (but I don't take photos). You can then finish up with the park early the next morning (if you want more time there) and still get to the Sea Organ and Tribute to the Sun in Zadar that day.

I like Zadar, but I think you can manage with one night there. Do investigate parking options. I believe the medieval center is pedestrianized, so you'll need to allow time to walk to it from wherever you have to leave your car (or grab a taxi). I mostly wandered around the peninsula that makes up the old town. Your daughters may enjoy checking out the shops. I might have been lucky with my timing, but there weren't a lot of other tourists there at the time of my visit in early October 2015.

Backing up to Istria: The little coastal hilltop town of Vrsar is cute. It's not in the same direction as Pula, but it's not far from Rovinj. Beyond Vrsar is Porec with its colorful, but touristy, old town.

I think covering Rovinj's old town, the beach and Pula in one day might be a pretty big ask. You can't just drive your car from place to place in old European towns and park it in the middle of the tourist zone.

I've never felt the need to go to Pula, not being interested in classical ruins. I did like inland Istria, which I was only able to see on a one-day bus tour. Motovun and Groznjan are atmospheric hill towns. They, too, are north of Rovinj. Personally, I'd much rather see the hill towns than a beach, but I'm not a beach person. As it stands, you might have time to squeeze in at least one of the hill towns, since you have a car. But Rovinj's historic district itself isn't tiny, and, again, there's the walking from the car (or from the hotel) to consider.

Check with your car-rental firm to be sure it's OK to take the car to Mostar. The bridge over the Neum Corridor in southern Croatia is now open, so you don't have to cross Bosnia-Hercegovina as you travel between Split and Dubrovnik.

By the way, I remember seeing a zip line in operation in Istria. I think it was in Pazin.

There is also a water park in Istria if that interests you or your daughters.

Thanks for the replies, suggestions. Yes, we will be picking up the car in Zadar.
Good suggestion on going to Rovijn first, then Plitvice Lakes. That change cut out 1hr 20min of driving!

My original plan was to drive from Dubrovnik to Split. Take day trips to islands. (I still might do this). But the suggestion to look into a catamaran to the islands and work way up to Split is intriguing.

Thanks!
Andy

You have a few unused days. Either spend more time in BiH by going on to Sarajevo or spend some time in Montenegro.

Herceg-Novi https://www.youtube.com/watch?v=dOqLXoeE_o4
Cetinje https://www.youtube.com/watch?v=r6RwWDPe9M8
Perast https://www.youtube.com/watch?v=fd6ErEHPHmg
Uncinj https://www.youtube.com/watch?v=LaPcThRQdi4
Budva https://www.youtube.com/watch?v=McNd2MTsDP4
Ostrog Monastery https://youtu.be/ixrJu6qv46M
& Hotel Sokoline https://youtu.be/8YJxe8Hv_y8
Tara River Canyon https://www.youtube.com/watch?v=9aGMZB8hB5Y

As someone who has driven to these places on a regular basis, with kids, I need to tell you that this is way too much.

Day 1 - you cannot tour Zagreb and drive to Plitvice in one day comfortably.
Day 2 - The lakes take all day. Following that up with a 4 hour drive to Rovinj on back roads is not feasible.
Day 3 - If you want to see truffles, you won't see them in Rovinj (note spelling) or Pula. To do Rovinj and Pula in one day is not feasible. There really aren't any beaches in Rovinj - just patches of rocks.
Day 5/6 - Zadar is fine, but not really that exciting. I wouldn't go all the way there for the organ, for sure. The drive from Rovinj to Zadar is looong.
Mostar - Maybe spend more time there if that really excites you?

Some tips/ideas:
Definitely cut out Rovinj and Pula - not worth the 8-9 extra hours of driving. As an alternative, consider Primošten on your way from Zadar to Split.
Spend more time in Plitvice.
You can see Trogir in 2 hours.
Definitely stay on an island. We really enjoy Brač, but your daughter may like the party atmostphere of Hvar. Coming back from Dubrovnik via Korčula also makes sense.

While in Zagreb enjoy a stroll on Tkalčićeva Street.
Sleep in Split’s old town and take day trips.
I would go to Istria before Split. The ferry from Split to Ancona operates four nights a week and takes 11h and you could rent a cabin to sleep in. However, getting from Ancona to Rome takes 4h but is direct. To get to Florence requires a transfer.
You do not need a car in Dubrovnik and I would take the ferry to Split. Mostar is not a day trip from Dubrovnik taking 3h 30m by direct bus. If I were going to Mostar I would also visit Sarajevo by direct train (2h), otherwise I would skip Bosnia & Herzegovina and visit another time.