Italy summer 2020 (already planning :) )

You are going to have an awesome time! As for flying and purely for the time saving, you should fly in to either Venice or Rome and fly out of the other to save travel time.
I would think a minimum of three days in Rome, with tickets to sites you wish to visit purchased before your trip. On a side note, see if you can get tickets for the tour beneath St Peter's if that holds interest for you.
Florence is IMHO magical. Museums and churches nearly everywhere, but again reservations are strongly recommended.
Florence is a very walk able city with discoveries around each corner.
As for the Cinque Terre, beautiful scenery but large crowds. You have the choice of hiking the paths between the towns or taking the ferry.
Venice is a place on to it's own and shines best early morning and after dark when the day trippers have gone.
No matter where you go, remember things run more slowly than at home and part of the fun is exploring and getting lost.
Enjoy

Best advice I can offer: Don't go in summer. It's shockingly crowded, and often miserably hot. Don't discount how much impact these things will have on your trip. Go in the spring or early fall and you will have a much better experience.

Think in terms of nights not days. I would fly into Venice and out of Rome. 3 nights Venice, train to Florence 3 nights, Tuscan countryside 3 nights, Cinque Terre 3 nights then Rome 4 nights A total of 16 nights with 2 travel days is 18 total. If you need to cut a day take it from the Cinque Terre.

Fly into Venice because water transport from the city to the airport can take longer than expected. You don't want to risk missing that flight home. Fly out from Rome because there's a fast reliable train between the city and airport (Leonardo Express from Termini). Also, though very crowded in the daytime, Venice is a relatively tranquil way to encounter Italy compared to Rome.

David is right about summer heat and crowds, but presumably you don't have a choice about when to go.

Thank you! I love getting advice on things like why it's best to fly in or out of certain airports. My 12 year old daughter is fixated on Cinque Terre and is doing her own research on it ;) She and her cousin, who will hopefully be joining us, would love to be able to swim at one of the beaches there.

There is a possibility of adding one more week to our trip - how realistic to add on a little of south France? I know that the beaches will be crazy busy during that time. Provence any better? to those of you that have been to both if you had to pick would you say Provence or Tuscany?

We would love to be able to go at a different time of year but are working around middle school and college schedules. We experienced Greece this past summer in July - it was very hot, but we managed. I actually almost started to get used to the heat after awhile :)

I always think more time is better, but I have a different suggestion for you: The Dolomites are beautiful, and if you stay at altitude, in a place like Ortisei, you will almost certainly avoid the intense heat that would be a problem in southern France. (The longer you deal with that sort of heat, the more draining it is.) The Dolomites are in the Alto Adige, an area with a strong Austrian influence in food, architecture, and language, so it's a lot like traveling to a different country.

The Dolomites have lots of great walks from simple strolls to more ambitious hikes, and there are some very interesting towns down in the valley, like Bolzano (the museum with the Iceman is there) and Bressanone. Just don't choose lodgings down in the valley, because it is just as hot as places farther south.

What a great sounding area! Is it bad that I don't think I've heard of the Dolomites?
My older daughter is a big hiker and would love to go somewhere like that. Thanks so much for the suggestion!!