Hello,
If you rented car in Trieste, Dubrovnik is about 7 hour drive on the fastest route which avoids Split and Plitvice.
Driving in Croatia is relatively easy. There are some winding roads but Trieste to Dubrovnik is mostly good highway, especially on the fast route.
Next question is how much of an issue is cost. If that is a problem look to see where you will fly out of first. Also unless it is really not an issue I would look at car rental from Rovinj or Pula and also from Trieste to see how much different cost will be. One way rentals are not always expensive but sometimes are very expensive.
You could easily do two nights Rovinj, one night Plitvice, two nights Split, two nights Dubrovnik if you want to see as much as possible. There is more to do near Split than Dubrovnik so I think two nights of each is about right in your instance. I also do not understand the advice of skipping Rovinj, it is highest or second highest tourist location in Croatia for a reason. I know you will have to skip something but it will depend on what you want to do.
You do not need two days to see Plitvice, two day ticket is more expensive than one day ticket and you can wake up and see the park with a one day ticket before anyone else visits. There was also advice about a park motel, I do not understand this, I have always stayed in decent lodging near Plitvice. So you would arrive at dusk, wake up, see the park, depart by lunchtime - that is not really two days.
A route with less driving might be a couple nights Rovinj, maybe a night or two in lovely Opatija or even on island of Krk, then a night or two in Zagreb and fly out of Zagreb. You could also switch Zagreb out here with Plitvice and Split, or even Split with Zadar.
Plitvice and Dubrovnik are probably two most spectacular touristy places in Croatia, but you can have an excellent trip. It is really just how much driving you want to do, how much rental car costs, how much flight back to where you are going costs.
By October there is only two daily catamaran Split to Dubrovnik I am aware of one leaving at 8:00 on Krilo lines and one leaving at 15:10 on TP lines. Krilo takes about 4:30 hours and TP takes 5:00 hours. I would probably skip this given your timing especially if you have rented car.