Rick Steve's 22 day trip in reverse-how to minimize train time

Florence to CT to Venice takes a lot of time no matter how you order it. The best strategy is to choose places based on your own interests. CT in July will be super crowded, and there are alternatives you could consider, especially since you are open to car rental.
Also traveling with a family requires a different pace--use the Rick plan as a general guide and tailor it to your group. I would not travel at that pace solo, and I cannot imagine doing so with two teens.

The two options you describe are equivalent, since you transfer between trains in... Florence to get from CT to Venice or vice versa.

However there's another option, depending on where in Tuscany you want to visit besides Florence.

You can take the train from Rome to CT: there are direct trains from Rome to La Spezia, where you connect to your CT town of choice. Such trains aren't the fastest but its more convenient than the fast train (with which you have a connection in Florence).

Then CT-Florence (rest of Tuscany) - Venice-Lake Como.
This avoids backtracking thru Florence.

Rick's 22 night itinerary is extremely fast paced- most here would call it totally exhausting and very unsatisfying. It consists of mostly 1 and 2 night stays. A 2 night stay means just 1.5 days actually being there- and that depends on how long it took you to get there in the first place. You'll be spending most of your time on a train/transitioning from place to place.

The itinerary allows Rome 2 Florence 2 Venice 2- those are all way too short.
Rome needs a minimum of 4 mights, Florence should have 3, Venice should have 3.

My point is- don't just follow that itinerary- decide where you want go- I'd probably drop 1 "water location" pick CT or Lake Como and if you don't have lodgings booked yet you may be limited by what is still available as those places book up very early.

A car will be useful in Tuscany but is not a necessity - day trips from Florence are quite easy by public transportation. With 4 people you will need to make sure the car you rent is big enough for all of you and/or luggage (luggage needs to be hidden if you are stopping/parking while in transit).

Do read up on driving in Italy- all drivers will need an International Driving Permit (IDP) you can get at your local AAA.

A recommended itinerary given your flights might be something like this:
Rome 5, Florence 3, Tuscany hill town of choice 2, another Tuscany hill town or Umbrian town like Assisi or Orvieto 2, Venice 3, Lake Como 3, Milan 2

That's still only 20 nights. Add nights to whichever place you are most interested in.
I'd probably add to Tuscany and do 2 hill towns there (perhaps 2 Siena and 2 Montepulciano).

Two-night stays yield a single full day; one-night an afternoon and evening. Linking a several of these is pure lunacy, resulting in seeing less than on a plan with longer stays. CT check the cruise ship schedule:

http://crew-center.com/la-spezia-italy-cruise-ship-schedule-2020

Also realize that when changing hotels a couple of hours are spent on top of the train trip. So e.g. CT to Venice 8 hours.

Thank you for your suggestions. I think I made an error when I wrote suggesting we were following RS's itinerary exactly, but to be clear we are taking it slower; we will be in Rome 4 nights, Florence 3, and Venice 3. We will go to Lake Como because we are meeting Swiss friends there (3 nights) and we will be in Milan (2 nights before returning to the US). This leaves us with 2 days (2 nights) in the middle of our trip and 3 days (3 nights) closer to the end, and I was trying to decide between 1) taking time in Tuscany on our way from Rome to Florence, 2) going to Cinque-Terra (if the travel time allows), 3) seeing the Dolomites, or 4) just spending more time near one of the cities we will be in already, perhaps Florence or surrounds of Venice. What I am hearing from people is it might not be worth going to two water areas which cancels our CT and slower is better, so perhaps seeing more around the cities we will already be in is best. . .

Again, thank you for the information you have provided so far. Its tricky to figure out what to do when there is so much to enjoy in Italy.

Christine H: Thank you for you suggestion. I like your itinerary and think it matches pretty well with our current bookings.

I would come down on the side of adding some of your days to Tuscany. The towns in the countryside are totally different from Florence. An agriturismo stay for a couple of days might be just the ticket with teen-agers. Also, it wouldn’t hurt to have another day or even two in Rome. Plenty to do and see there. If you go to TripAdvisor, put in the name of your destination, and click on “things to do,” you will see that there is much to see in all the places you have mentioned, probably more than you’ll be able to do.