Help with travel from Dubrovnik to Pula

Is everything all booked? If not, I would change it up and immediately take a local Croatia Air flight to Dubrovnik so you can work south to north.
Otherwise, lots of options. You could go from Dubrovnik to Korcula for your island stay (by bus or catamaran), then head on to Split and take a bus to Pula from there. You may have to change buses in Zadar. There are probably dozens of other options, just depending on how long you want to spend on the road in one day.

I'm assuming your flight into Zagreb and your ferry out of Pula are locked in, but are you committed to the rest of your itinerary? Do you already have reservations for lodging, and if so, can you change them?

If you have some flexibility, I would suggest moving things around a bit. Maybe something like this (showing where you sleep each night):

21-22 sleep in Zagreb,
23 fly to Dubrovnik
23-25 sleep in Dubrovnik
26 ferry to an island of your choice
26-27 sleep on the island
28 ferry to Split, visit Split, pick up rental car, drive to Trogir, sleep in Trogir
29 half day in Trogir, then drive to Plitvice, sleep in Plitvice
30 Plitvice N.P. in the morning, then drive to Pula and drop the car there, sleep in Pula
31 ferry to Venice

The reasons I suggest this are (1) you should plan on an early morning visit to Plitvice NP to beat the crowds; (2) drive from Plitvice to Dubrovnik is very long, making 24 a difficult day if you visit the park in the morning and then drive to Dubrovnik.

If you're stuck with reservations you've already made and not flexible to change things around, You might still consider renting a car in Split after spending some days on one of the islands. It might be possible to use public transport to get to Pula, but I'm not familiar with that, and with four of you, driving might prove more economical.

Thanks so much for the advice. I did have some reservations made but am able to change them. We will fly from Zagreb to Dubrovnik for 3 nights, bus to Split to island of vis for 2 nights and back to split. Rent a car and use split as a home base until it is time to leave for pula. Not sure how we will get to pula, car rental or bus but will look into both. Thanks again! What an excellent site for help with travel!!

Don't skip Plitvice! And doing that in high season really means spending the night before the park visit right at the park, not in Split.

Try to head in one direction rather than having to back track to Pula.

Much accommodation on the islands has a 3 night minimum booking.

Although Vis is pretty, it's the hardest island to get to from Dubrovnik and will take over 9 hours door to door. IMO not worth it just for one full day there! If you want hiking, Mljet would be the best island to stay on - a great National Park for walking. Then catch the daily catamaran after your 3 nights to Split - krilo.hr for reservations.

Krka is as stunning as Plitvice with fewer crowds, as an alternative.

Split and Trogir are worth a day each to explore.

Your best option to get from Split to Pula is to keep the rental car and drive. With 4 people, that's much more efficient than using public transit or flying. I looked into various options when I went from Split to Rovinj and decided driving made the most sense. Because my rental was 3 days or more, I wasn't charged a drop-off fee. If you still plan to go to Plitvice, I'd suggest driving there on the afternoon of August 29, having dinner at Licka Kuca (across the road from entrance 1 - the grilled trout is outstanding), visiting the park early on August 30 and then driving to Pula in the afternoon. The direct drive from Split to Pula is fairly long (6-7 hours with stops), so you might prefer to divide it into 2 approximately equal segments by stopping at Plitvice on the way. It also saves you a long day trip to Plitvice from Split.

Reread acraven's comment about Plitvice lakes at least three times. We have been over most of Europe and find those lakes almost on par with our favorite place in the world, Rome-one of us is a psychotic Roman history buff. We spent three days at an Airbnb cottage (there are several places to visit). The place is simply magical. Loved the amphitheatre at Pula (drooled over it), but would still pick the lakes.

In addition to other suggestions, we will have catamaran service from Zadar to Pula from some unconfirmed date in June. There will be island stops on the way for those who want to break their journey.