Itinerary help

Fly to VCE. Take taxi(or bus)+boat to Venice Hotel. visit Venice= min. 2 nights Rent a car in Venice after visiting Venice and drive to Dolomites (better have a car for Dolomites). Visit Dolomites= min. 2 nights Keep car and drive from Dolomites to Val D'Orcia in Tuscany (better have car in Tuscany). Val D'Orcia= min. 2 nights or more depending of how much of Tuscany you want to see. (Keep the rental car) Drive from Val d'Orcia to La Spezia. Return rental car in La Spezia. Take short train ride to Cinque Terre. Cinque Terre: min. 2 nights. Take train from Cinque Terre to Roma. Roma= min. 3 nights.
Fly back to the US from Rome. If you don't go to the Dolomites, then you can take a train from Venice to either Florence or Siena and rent a car there. Or if you want, you can still rent in Venice and drive from there (about 4 hours from Venice to Val d'Orcia, mostly easy freeway driving). It also depends on how many people are traveling together. 3 or more people traveling together will probably save $$ by driving over taking the train. The above suggested nights in each place are the absolute minimum. I'll let you allocate your available nights on the ground (I used only 11 nights on the ground in my suggested itinerary above) depending on what your preferences are. Some people like to spend more time in Venice or Rome, others prefer more time on the coast (Cinque Terre), others would rather spend a long time in the mountains (Dolomites) while others prefer the Tuscan towns and countryside.

Roberto has given you an excellent framework. I would only differ to say you do NOT need a car in the Dolomites. We have gone there sans car twice and love the freedom of not having a car. Do spend at least 3 nights in each place as you have the time. The Dolomites will be your refreshing cool stop during the hot season, so make the most of that respite. I have written about our time in the Dolomites here and here.