One issue might be getting from Positano to Naples for the flight home. It is a bit of a trek. Depending on flight time, you might need to be in Naples the night before or get a private driver to take you to the airport.

Rome: You will have max, a day and maybe 3/4. Use taxis and plan well, getting tickets ahead, or get a tour that gets you in and out of places without waiting in lines for tickets. Otherwise you will see very, very little in Rome. Sad, because Rome, with beautiful fountains, centuries old sculpture and some of the most significant buildings in the world will mostly be missed. It is a city that needs a little time to be appreciated.

You will use a good 1/2 day getting to Positano. Did you want to see Pompeii or just a bit of the AC? Seems a shame to go all that way, spend time and money doing so, and not see some of the most iconic sights and have time to enjoy what the AC is know for - relaxing and enjoying the magnificent views.

10 days is decent for Venice, Florence and Rome. Why spend so much of your time rushing right past fabulous sights? Sienna, Luca, Pisa, Rome. You are going to see less, not more, with this plan.

Stretch your trip to 12 days, or cut something, or -
Are you really big into Art?
If not, depart Venice early, stop in Florence, stash luggage at the train station, spend six or seven hours, go to Rome late, get a taxi to your hotel.

What time of year is your trip? Winter months mean shorter daylight hours, which can affect your plans.

I have learned that most people who go to Rome are convinced that they have to see the Vatican Museums (where the Sistine Chapel is) and the Colosseum. These are not my favorite things in Rome, and on a short trip I would recommend skipping both of them. They're both very exhausting visits, and usually extremely crowded.

If you're willing to "see" Rome without visiting those two places, you could have a pleasant stay in Rome with only two nights. However, if you insist on seeing those, then I would advise you to spend more than two nights, or you risk seeing only thousands of tourists who are invading your personal space, as you're invading theirs.

If you're not much interested in art, you could make Florence into a six-hour stopover, without spending a night there, and add two more nights to Rome. You would leave Venice early in the morning, put your luggage in storage at the Florence train station, and proceed to Rome in the late afternoon, after picking up your luggage. Florence is a small city and can be easily "seen" if you don't need to see any of the museums. (You could still see plenty of Renaissance art in some of the churches of Florence.)

Or you could take Sandralist's advice and cut back on Positano. I agree that it's not a place that would lure me back. However, I know people who go there every year and love it.

However, you first need to decide what you want to see and do in each place you visit. Other people will tell you what you "must" see, but they really don't know what you'd enjoy. Would you let perfect strangers pick your wardrobe?

Thank you all for your replies and input!
We finally booked and we're very happy with our selection:
Venice 2 nights, train -->
Florence 1 night, train -->
Rome 3 nights, train/driver to
Almafi 3 nights
We're in the process of mapping out what we want to see and do. There's so much! I will report back on how this itinerary worked for us!

Thanks for reporting back and looking forward to your trip report!

I don't think you mention when you are traveling, but there is a ferry that runs from Salerno to Amalfi to Positano until around Oct. 31, when it quits for the season. It starts back up on April 1.

It can be very convenient to take a train from Rome to Salerno, and then take a very short walk to the ferry pier. I did this from Naples years ago when I was on a cruise.

Very nice!!! (and thanks for checking back in w/ us!) Have FUN.