We travel by car to Dubrovnik from the UK every summer, we drive a VW Passat, and although it is a three day trip it is perfectly straightforward.
What you have probably heard about Croatia is the coastal road that runs from Rijeka to Dubrovnik, which is not built to motorway standards, nor is it a dual carriageway. Provided you accept it for what it is, it is a perfectly good road, but it is slow.
The good news is that two or three years ago a new motorway was constructed from Zagreb to Split. This means that from Bratislava you will be on motorway all the way to just past Split except between Maribor, Slovenia and the Croatian border. Provided you don't mind some long tunnels the journey is fine.
All that said, the ferry down the coast is great too, as it stops at a number of lovely islands.
However if you want to get a feel for the place, don't use the motorways, use the inland regular roads. It takes more time, but you'll see much more.