I've not done this trip, although it's floated up my destinations list and hopefully will be something we can do in a few years.
You've an awful lot of travel packed into two weeks, and the only efficient way to do much of it is to rent a car. You can do it by buses and trains, but that would add days to the journey and take away from your valuable travel experiences. So while expensive, a car will help you get the most out of your travel days and with three people won't be prohibitively expensive,
If you're going to rent a car for 3-4 days, you might as well rent it for a week because the rates are the same after the 4th or 5th day (you get charged the weekly rate). Drop-off fee will almost certainly be charged but it beats making a loop drive (given the high cost of gas and the time wasted). Driving should be pretty straight forward but it will definitely pay to have a navigator with a GPS to help you out. It's very easy to get lost with you get off the Expressways.
Typically I'd rent a car at a big airport (never get it when you land from America == the jet lag makes you a dangerous driver). Take a day or two or three to recover and enjoy Venice and then pick up the car and begin your journey. End at another airport, possibly Ljubijana, and look at option of doing day trips from there to end your trip. Maximize the week with the car to see those remote destinations that are otherwise hard to get to.
Let us know how this works out. It's a beautiful part of Europe I really want to see.