Slovenia and Croatia for 13 days,too much or too rushed?

If you opt for driving to Split from Rovinj, the fastest route takes 4:40. You could stop in Sibenik, a gem of a coastal town about one hour from Split. You also could visit Krka National Park which is just 15 minutes from Sibenik.
Dubrovnik is a 10-hour drive from Rovinj.
Have a great trip!

It does feel a bit rushed, and really it’s Dubrovnik (and Split really) that’s doing you in. They are both outliers from the bulk of your trip and what seems to be your focus. I wouldn’t go further south than Istria. You might want to consider Piran as an alternative to Rovijn, which is closer still. But heading all the way down to the Dalmatian coast is a mighty detour.

There’s so much to see around here, and it’s so spread out. That’s what makes planning so challenging. I would tighten this trip up to Slovenia, maximize your experience there. Then bookmark Dubrovnik up the coast to Split etc, etc, for a future trip.

I would look for a way to wrap up in the north versus going to Split or Dubrovnik. Where were you planning to drop the car?
The sea starts to warm at the end of May, so some coastal time would be a nice cap off. If earlier in May, enjoy those days in Istria and see if you can fly out of Pula, Rijeka, Zagreb.

In Slovenia, you're missing the Julian Alps.

I'd split up the cave trips, and they are close enough to Ljubljana to just visit from there.

Consider Opatija over Rovinj for the Adriatic, then visit Plitvice Lakes and end the loop through Karlovac to Zagreb.

You should not miss Plitvice Lakes-I've never seen anything like them or like Lake Bled. I wasn't a big fan of Split. Apparently you love caves but for I didn't see anything special at the one we went to-I think Postojna. It wasn't any different than caves I've seen in the US.