Northern Italy, Slovenia and Croatia

As long as you will be returning the car in Italy, there shouldn't be a problem with taking the car to Slovenia and Croatia. Note there may be some limitations that vary between companies, especially regarding the make and model, but you should be able to work something out relatively easily. Make note of the various requirements for driving in each country, such as the toll stickers (vignettes) in Slovenia and Austria, etc.

Since you'll be travelling in August, the more popular places will definitely be crowded, especially Venice, which will be absolutely swamped with tourists. You may alleviate that by going to some of the less busy outer islands, such as Burano, but if you dislike the crowds and if possible, save Venice for a later spring/fall trip to Italy. Of the four places you wish to visit, I suggest picking just three - two weeks is not as much time as it sounds. Also, don't venture too far south in Croatia if opting for it, I would only go as far as Istria and possibly Plitvice Lakes or Zagreb, although the latter two will be a bit of an investment in terms of time that you may not be able to afford if you stick to all four regions. Plitvice will also be extremely busy during your visit, right after Venice - even Lake Bled doesn't get as crowded in my experience.

In the Dolomites, you have a number of places you can visit. I would choose one town as a base to explore. Be conservative here, the Dolomites are a large region, much larger than Slovenia's Julian Alps, don't overextend yourself. Also, with a car, you don't have to stick to the more popular towns, you can easily book accommodation in a neighbouring town or a couple of miles away. It might make all the difference when it comes to crowds and can also be easier on your wallet.

In Slovenia, the main places to visit are Ljubljana, Lakes Bled and Bohinj, the Soca Valley (with the mandatory scenic drive over Vrsic Pass), Piran and one of the caves, such as Skocjan or Postojna. If your kids love horses, make sure to visit the Lipica Stud Farm, one of the original homes of the Lipizzaner, better known as the horses from the Spanish Riding School in Vienna. There are also plenty of activities that your kids can enjoy in the mountain areas, such as adventure parks, summer tobogganing in Bled, cycling, swimming in one of the lakes, etc.

Dejan, I cannot thank you enough for your quick, thoughtful, wise and detailed response. I hear you about August--we are stuck with that timing since kids are off school. We are trying to tighten up our itinerary to a more compact area. What do you think about this?
Two nights in Venice, three nights in the Belluno area to enjoy some Dolomite scenery, three nights in Bled area and then on to Istria for four nights and back to Venice for one. I am hoping that is not too much moving around--otherwise we remove one of those destinations. Is there a nice place in Istria to use as a home base and then day trip to beaches or hill towns? We are very open to any location in Istria...
Thanks in advance for your invaluable advice!

Two nights in Venice means only one day there, which maybe needed to get over jetlag. With the crowds in August, it won't give you long to see anything.

You have 5 locations in 13 nights, which IMO is too much moving around and not enough time actually seeing places, particularly as you are not flying open jaw and are losing a day having to get back to Venice. I would recommend that you drop Istria or Italy. Istria is the obvious, due to its location furthest from Venice.

Inland areas won't be as busy as the coastal areas, but August is a busy month and places are getting booked up.