15 Day Itinerary May/June

I always advise not including both Cinque Terre and the Amalfi Coast in the same itinerary because you can get the same things out of just one or the other. There are coastal hikes all over the Amalfi and Sorrentine coasts and on the islands. You are already there for Pompeii, so I would just extend time there. Then you would not have to spend all that time on the train between CT and Venice. To me, that is just wasting valuable vacation time that could be spent doing stuff.
Naples to Siena will be a long day, so you may not be able to see much of Naples. Check schedules on the Trenitalia website, but I think for Florence to Siena bus is better. Driving in rural Tuscany is really not the horror show some make it out to be.
Unless you especially want to see the Duomo or last supper, I would give Milan short shrift and arrive the day before departure. I'd want another day in Venice.

Totally second valadelphia's comments. Skip CT if you're visiting AC. Naples to Florence is much easier. And we drive all over Tuscany it's pretty easy. BUT if you do stay in Siena, I highly recommend Tours by Roberto.... NO one does a better tour of Siena. We had visited Siena twice before we took his tour ... holy cow it was amazing.

5/23: Roma Termini to Napoli Centrale, the downstairs to Garibaldi and tickets for the Circumvesuviana train to Pompeii Scavi; store bags on lower level. Then back on the train. Have your valuables secured under your clothing and hang own to your bags.

5/26: I’d have a driver bring you to Napoli Centrale, baggage drop ahead and to the left. Siena is a problem—train 5 hours on 2 trains; Cinque Terre from there 4 hours on 3 trains. Then packing up in a CT hotel and unpacked and walking out of the Venice hotel plan on spending +-8.5 hours.

You are in Italy for 16 nights and visiting seven places (including Naples). I would suggest that you cut that down to about four. Also, as suggested above, add up all your travel time, with this current itinerary you'll spend a lot of your vacation time packing, unpacking, or on a bus or a train.

This is an ambitious itinerary. You are at least one day too few in Rome and should skip CT altogether. Amalfi>Rome>Siena>Venice would be my recommendation. Fly in to Rome then train to Amalfi (get that travel out of the way). Fly home from Venice. That's my $0.02

Alright taking a shot at this again. I've removed Cinque Terre and using more home bases to do day trips

May 20: land 8am in Rome (stay in Rome)
5/21: Rome (stay in Rome)
5/22: Vatican sites and Rome (stay in Rome)
5/23: Leave early for Pompeii and continue on to Sorrento (stay in Sorrento)
5/24: Sorrento and explore Amalfi Coast or Capri
5/25: Sorrento and explore Amalfi Coast or Capri
5/26: head to Naples for the day and head to Florence for the night
5/27: Day trip to Siena (stay in Florence)
5/28: Rent a car to explore part of Tuscany (stay in Florence)
5/29: Early morning train to Venice
5/30: Venice
5/31: Venice
6/1: Leave Venice early AM and stop in Padua or Verona for half day (stay in Milan)
6/2: Day trip Varenna (stay in Milan)
6/3: Milan or another day trip (stain in Milan)
6/4: Fly out of Milan

Think could maybe just stay in Varenna 6/2 also and head back to Milan the evening of 6/3 or early enough to try to see Duomo and Last Supper