Venice-Tuscany-Amalfi-Rome Itinerary Suggestions

It's about 325 miles from Rome to Venice, and taking the train that far after flying in from Chicago would be more than I would undertake. It might be a little tough on your parents too.
Pisa would be a good day trip since it's an hour by train west of Florence. We, like many others, bypassed the Leaning Tower last time we flew into the Pisa Airport.
Siena is a popular day trip by bus from Florence. The buses are out the side door of the train station to the right of McDonalds and around the block. They take you into the Siena center city, and it's about a 1 hr. ride. Trains are slower and drop you on the edge of town.
Many people take the train down to Pompeii from Rome (150 miles) and connect to a local train that goes to Pompeii and out to the Amalfi Coast. Parking is tough to find on the coast, and the roads are tough to drive--congested and crooked.
When traveling, we try to fly open jaw to the far end of our trip and work our way back--in as close to a straight line as possible. It would have been much more efficient to have flown into Naples and out of Venice.

You have two weeks. In my experience that means four over night places. I think you have way too much planned not even considering that your parents are older.

I loved the Amalfi Coast but I don’t think you have enough time for it. I would delete it and slow down your pace.

I have friends who spent two weeks in Italy at a frantic pace. They got to Pompeii and didn’t even go see it because they were too exhausted. Pompeii is an all day activity once you travel back and forth.

Italy Itinerary can be set like this:

June 13 - Depart

June 14 - Arrive in Rome FCO 7:30 AM; train to Venice (need train advice; this is non-negotiable as connecting flights were too tight
and Dad is super excited about train travel in Italy)

June 15 - Venice (or Vicenza to visit ancestral home)

June 16 - Venice )or Vicenza; is it better to visit Vicenza Saturday or Sunday? We need to take public transit)
Visit Vicenza on a Sunday because Saturdays can be busy with wedding parties and Villas will be crowded.

June 17 - Early train to Pisa; see the Leaning Tower; then Train to Lucca, pick up rental car in Lucca and drive straight to lodging near Volterra.

Next four days: we want to see Florence and Siena for sure. Best day to go? Other "must see Tuscany" stuff that won't lead to exhaustion?

June 18 – Volterra - Day trip to Florence

June 19 – Volterra – Day Trip to Siena

June 20 – Volterra – Day Trip San Gimignano and San Miniato

June 21 – Volterra – Day Trip Castellina in Chianti

June 22 - Drive to Amalfi/Vietri Sul Mare

June 23 - Pompeii and Herculaneum

June 24 - putter around Vietri? Other ideas? explore Ravello

June 25 - Drop rental car in Salerno; boat tour of Amalfi Coast (recommendations for a boat tour?) http://www.amalfiboats.it/

June 26 - Morning train to Rome; AirBNB near Vatican (maybe Borghese Gallery in afternoon?) Book tickets in advance for afternoon at Borghese Gallery

June 27 - Early entry Vatican tour (suggestions for afternoon?) Do an afternoon 2pm tour, less crowds at that time then morning.

June 28 - Morning Colosseum/Roman Forum/Palatine Hill tour (afternoon or evening suggestions?) spend evening in Trastevere Neighborhood.

June 29 - open for suggestions (Day Trip from Rome to Ostia Antica - Train)

June 30 - Depart FCO on 11:00 flight

If your parents stamina is a concern, you may want to look at deleting the AC area ( too far from the rest of your destinations) and instead substitute Cinque Terre for your 'seaside' experience.

You could do Ostia Antica as a more than adequate substitute for Pompeii.

Since you arrive so early taking a train to Venice is a good idea. Excitement will carry you far, but it is easy to nap as well. Generally we advise to not buy tickets Rome to Venice until you have passed through passport control. There are many trains each day, but the 11:08 is direct with no change at Termini so it might be worth biding your time at FCO for that train.

and we have also wondered about just leaving some days open and letting fancy take flight. However, we aren't sure if this is unwise, the whole "failing to plan is planning to fail" thing

I think many, in an effort to see it all, end up not "seeing" anything. They approach visiting Europe like those who try to ride every Disney World ride in a day. Everything is a blur and you wind up exhausted.

It's the old "quality vs quantity" paradox. Our trips, both in Europe and in the US are much more enjoyable when we plan in down time. We try to schedule every third day as a "down day", with little or nothing scheduled. This allows some spontaneity in the trip and possibility to experience something we stumbled upon but couldn't enjoy if we had to be off on another adventure.

When I think back on our trips, the most meaningful moments were usually the unplanned. These are experiences we could never anticipate before traveling but we can enjoy because of a loose and (somewhat) flexible schedule.

Keep in mind you will be going during peak season. It will be warm to hot and everything will take longer because of the crowds. You probably will go at a slower pace because of your parents. When visiting Siena, Florence and maybe Rome, consider having at least one day where you travel as a family for half the day and let your teenager and your parents head out on their own for the rest of the day. That way your 19 year old wont feel tied down by your parents.

I agree with others, you've got too many stops and location changes. I'd drop everything south of Rome and add the time to your lodging near Volterra and your stay in Rome.

I would definitely stop in Lucca. It is a nice medieval town, have a leisurely walk along the wall (nice and flat), have lunch, then go to your lodging.

As far as Volterra, it is one of my favorite towns, but you have to park at the bottom and walk up about 300 steps. Don't know how your parents would do.

I agree with others, Pompeii in itself will be a long day. And hot! Bring water, sunscreen, etc. Maybe skip Amalfi.

When in Rome, explore Trastevere and the Testaccio market. http://www.mercatoditestaccio.it