Having visited Plitvice (for the third time) in late August 2015, I urge you to arrange your trip so that you spend the night before your visit in the area near the park. The park gets unbelievably swamped. I waited in line for over an hour just to buy my ticket. The tickets aren't timed, so anyone who wants to get into the park can get in (eventually). It was a mob scene like one might experience in the Vatican Museums or the Louvre. The park is extremely nice and it's as close to a must-see as any place I've ever been, but it's essential to beat all the day-trippers onto the walkways. That means you should not treat Plitvice as a day-trip from Zagreb, Split, Zadar, etc.
If you get started when the park opens you'll have plenty of time to drive on to Zagreb (less than 3 hours without stops, according to ViaMichelin) or to Ljubljana (a bit over 4 hours) after your park visit. I mention Zagreb because 1) You'd avoid the cross-border drop charge by returning your car there; 2) It's a very nice city with a lovely old town very much worth a visit; and 3) There's rather frequent bus service to Ljubljana, trains being less frequent. The buses are quite nice. If you decide on a stop in Zagreb, your daughters would almost certainly enjoy the Museum of Broken Relationships, just one of the interesting museums in the city.
You can check rail schedules on the Deutsche Bahn website and bus schedules with BusCroatia.
Other Croatian cities where you might be able to drop the car and get a bus or train on to Ljubljana are Rovinj on the Istrian Coast (very picturesque, very touristy, buses only) and Trieste (haven't visited, but it has both bus and train connections with Ljubljana, trains being faster). Transportation to Ljubljana from Rovinj and Trieste is rather infrequent. Neither of those options would be faster than going to Zagreb, however.
Bus schedules can vary a lot with the day of the week and should always be verified once you are in country. Cross-border tickets should be purchased ahead of time, because those buses can fill up.
You'll find that English is widely and well spoken by the younger folks in both Croatia and Slovenia, so working out the logistics will probably be easier than you are anticipating.
Edited to add, in response to Tim's suggestions:
Mostar is great and would be an excellent day-trip form Dubrovnik.
I enjoyed Zadar a lot for half a day and would have liked to spend the night there. It has a wall like Dubrovnik, but you can't walk round the city on the wall. A plus is that it doesn't get as many tourists.
Pula is know for Roman ruins and is a popular tourist destination, but I haven't been there. It would be quicker to reach than Rovinj.
I've only passed through Opatija on the bus. It's my impression that it's an old-line resort that doesn't get a lot of youthful visitors and might not be particularly appealing to your daughters, but I might be totally wrong.