I can guarantee the actual travel times will be much longer: meal breaks, "releaf" breaks, justified meltdowns by super fatigued children, road works, paperwork delays at the border crossings because of the rental car, and a million other things. The travel times for some of those legs will be as long as twice the estimate which does not allow for stops and problems. You will be left with 10 minutes visiting each city or area, instead of, say, 4 days. You need to either make this a 20-to-25-day trip, or limit yourself to one, maximum two destinations.
Please note that the car rental companies have a blacklist (countries where you are not allowed to take their car). If I remember correctly, Eastern European countries make up the majority of that blacklist.
Last May we had an unforgettable 10-day trip in Italy. We stayed in a total of 4 places. We had a really wonderful time and some of the places we visited are breathtaking. That said, if we had been able to stay two weeks instead of 10 days, that would have been even better.
If you are interested, I can give you our beautiful itinerary (but for the length of your trip, I would recommend to only do about half of it, otherwise you will miss some of the best things in each area). A circle from Venice to Venice, including the Dolomites and several other wonderful places in the North-Eastern parts of Italy. No border crossing headache or insurance problems. Let me know if you want to see it.