You're going to fly 17 hours then go to the train station for another couple of hours to Naples? How many time zones are we talking about? With this itinerary, you'll spend at least half of your two weeks actually in planes, trains and automobiles, and you'll be exhausted doing it. For example:
day one: arrive Rome, By the time you pick up bags, go through immigration, go to train station, take 1.5 hour ride to Naples, pick up a driver and head to Sorrento, find hotel and check in, I'd bet it's day 2. Are you planning on sleeping at all?
day two: OK, so you've made it to Sorrento and/or Positano. You could kill 3 days there, for sure, but why? Pretty, but not for 3 days, In my view. But then again, trying to drive the Amalfi Coast in mid-May, it probably will take 3 days.
days 4-6: it's another 4 hours on the train to Florence.
days 6-7: Florence to venice for one night? You'll have enough time to find a hotel, check in and eat dinner. Sleep. Then you're off again.
days 7-10: Venice to Slovenia. Best case scenario, it's a 2 hour drive, more like 6 or 7 on the train. If there's a ferry, it would go to Koper, which is at least a couple of hours from Ljubljana. Overnight in Ljubljana.
Pick up the car at the crack of dawn and drive to Bled, walk around the Lake and keep going. Through the Julian Alps to Rovinj, at least 5 hours without a stop.
Get to "Istria". Spend a day in Rovinj, then back in the car.
Days 10-13: My apologies, but this is just lunacy. Rovinj to Split, driving 5 to 8 hours. Split to Mostar, at least 2. Going back to Split? 2 more hours. Split to Zadar, about 2 hours, 2 more to return. R/T Split to Dubrovnik, a good 8 hours. Day trips? Mostar, probably. Zadar, possible. Maybe, if your idea of a day trip involves driving most of the day, spending an hour looking for parking, spending an hour ( maybe two) at the sights, eat, and returning to Split in the middle of the night. And, are you planning to see anything in Split?
Then back to Rome for 2 nights? Where you will take a shower and collapse until your flight home?
Very ambitious, no, very impossible. What can you actually see/do in a few hours anywhere? Are you planning to do one sight before moving on? You're not factoring in reasonable amounts of time for any logistics. Think about it--hotels in and out, moving from hotels to transportation, waiting for transportation, 2 hour meals, accounting for traffic, getting lost, border crossings, bathroom breaks. How long does it take to do these sorts of things in Singapore? And that's, presumably, with your being familiar with everything. And you're traveling with 4 people. Just getting in and out of the shower every day will take the family at least an hour. That's just a short list. Even if you had a personal car and driver and guide for the entire time, it wouldn't work. I hate to be Debbie Downer here, but I think it would be seriously hopeless to accomplish this itinerary with any degree of satisfaction.
With some ruthless editing, this is itinerary is salvageable. I'd suggest picking one country. You'll be pressed to do any of them justice in two weeks. Let us know how you decide to proceed.
