I am trying to figure out the fastest way to go from Split to Hvar via car ferry, stay a day or better yet a night, then go by car to Korcula for two nights, then get to Dubrovnik for a few nights before driving to Montenegro and Mostar. After that I come back to Dubrovnik for the night and an 8:30 flight to the states. The car is causing problems. I do not really want to return it early in Split. Renting again in Dubrovnik for the Bosnia, Montenegro parts would waste time and be expensive since this all will occur in the latter part of Sept, 2018 which is only about a month away from this post. I have not priced the Dubrovnik rental however, so if someone is knowledgeable about short term rentals please weigh in.
Buses and ferries are good choices, as are local guides. Neither Split nor Dubrovnik are car friendly. Both are small cities. You can walk all over the parts that you wish to go to. In Dubrovnik there is the old city (no cars at all) and the new port (accessible by bus or walking - it took us 1.5 hours to walk from the old city which was interesting). A car can be used in Split, but again why? Split - Dubrovnik - there is a ferry for little money. Hvar and Korcula are islands. You can't go there with a car. From Dubrovnik, there is an inexpensive bus to Kotor and also to Mostar. Unless you have a lot of people in your party, I don't see the car as required for any part of this trip.
I don't know where Paul gets the idea that you cannot take a car to an island (two large islands at that), which I would highly recommend IF you were going to be there several days so you could explore the island with it. For just a night or two, I really do not think it will be worth the hassle. Once you add up the time investment plus the increased ferry costs, you might find it equal to just renting for the Montenegro and Bosnia portion.
Are you touring Istria before Split or just using the car to stop at Plitvice--the latter can be done easily with bus as well.
If you decide to go with catamarans, the operator is Krilo. Jadrolinija operates car ferries as well as catamarans.