Thank you again. I originally posted my question under general Europe by mistake.
Here is our modified itinerary: April 16-23
Our flight arrives in Venice 1130pm on the 16th. We were originally only planning 2 nights in Venice but with the later arrival and jet lag, thinking about 3 nights there.
Then leaving early to catch train to Cinque Terre for 2 nights. (I understand it takes roughly 4 hours-going though Florence) Then take the train to Rome and spend the last 3 nights there. (approximate train time CT-Rome? 3.5-4.5 hours ?) Flying out of Rome at 8am on the 24th.
Our only other question now- do we consider stopping in Orvieto to spend one night on the way to Rome. It sounds like such a charming little town. That would leave us with 2 nights in Rome. Or consider just 2 nights in Venice instead of 3.