A good itinerary

As it sounds like you already bought the tickets to/from Rome, which is far from the most convenient start/end point for where you want to go, its time to make some lemonade

A loop, Rome-Venice-Dolomites-CT-Rome, to me makes the most sense. Frontwards or backwards see no real advantage/disadvantage to direction of travel.

Just plan to be back in Rome the day before your flight back home.

With the exception of the Dolomites trains work well for your travels.

Depending on how you are counting '12 days' ( does that include or exclude your arrival and departure days?) , adding any other places 'along the way', may not be practical

I agree with Joe. Everything you listed is in the north of Italy and you're flying into the south so unfortunately you've added some extra train travel onto your trip. It's still doable but I'd drop the Dolomites as it's just not easy to get to and your time is limited. The Amalfi coast is south of Rome and easier to reach. It also has beautiful views. Perhaps that could be another alternative.

Hi Jill, and welcome to the forum.

joe32f has given you a great path, but you could simplify it a bit by going from the Dolomites to the east side of Lake Garda rather than the (Cinque Terre 6.5 hour train ride)

Look at these towns along the lake, Riva del Garda, Mescaline, and Peschiera del Garda then travel back to Rome from Verona (2:53 trip)

Is trip 12 nights or 11 nights?
Count your trip in nights not days.
What time do you arrive in Rome, what time do you depart?
Are you traveling from the US?

Suggest you go straight to Venice when you arrive in Rome, then do the loop as Joe as suggested returning to Rome and put all your Rome nights at the end.

I'd say you should allot 3 nights to Venice and at least 4 to Rome- leaving only 4 (or maybe 5 nights?) for both Dolomites and CT is really not enough.

OR
Since you are in/out from Rome- might reconsider and look to the south of Rome?

Expect lots of crowds in the Cinque Terre. You may be better off going to one of the lakes. Or just going to the Dolomites and Venice and Rome. For historical places, Rome is classic and you need 2-3 days there. Even if you have 12 nights in Italy (11 days), you will be traveling for much of a day to get to Venice, to the Dolomites and to Rome. That leaves you 8 days. 3 days in Rome, and 5 split between Venice and the Dolomites. 4 destinations is too much.

There is train service to Bolzano, then you may want a bus to somewhere closer to the Alpi di Siusi, for beautiful scenery and hiking. The RS tour I was on stayed in Castelrotto (Kastelruth) and we took the local bus to another town to board the gondolas and then lifts up to the hiking trails. I'm sure there are other beautiful areas in the Dolomites as well.

You could go to Venice first, then train or rent a car up to the mountains, then return the car somewhere before Rome and hop on a fast train.