We did the opposite route one year ago although we dropped the car in Rovinj instead of Pula to get to Venice. (I did get lost in Pula though). From Rovinj, and Pula as well, it is an easy drive to Plivitice. Almost all freeway. I would only spend one night in Plivitice as you can walk the park short of three-four hours. Try to stay close to gate number 1. There are several recommendations on TA for Plivitice accommodations. Most people like Split but it really wasn't my cup of tea. We hurried through it in a morning. The drive down to Dubrovnik is wonderful and beautiful. Don't forget to spend time in Ston and Mali Ston for some oysters. It will take some time to drive due to the curve- nature of the road but you will not regret it. If you are into botanical gardens, there is a best kept secrets just 20 mile north of Dubrovnik. Do you have your lodging squared away in Dubrovnik? You may want to try this web site for car hire in Pula. There is usually some satellite
office near the port. If not, you can taxi into town.
Depending on the day, you may consider a ferry from Split to Dubrovnik. It is also a beautiful way to travel.