16 day itinerary for April 2018 - comments welcome please

Given that you are mainly visiting larger cities, I would consider dropping the idea of renting a car.

It looks to me like you plan to spend a great deal of time in transit vs time at destinations. Those two night stays don't give you two days, at most a day and a half. The drive from Tuscany to Sorrento, in particular, is quite long.
First I suggest you check out what the weather is likely to be at the Lakes in April. Not much to do if it's raining. If you omit the Lakes, you should have time to add to Florence and Rome.
There are a couple of huge garages for Venice parking, but getting from Venice to Florence by train is easy and inexpensive. There are some garages at the periphery of the Florence ztl zones, which have a daily rate of 20 euros; but you'd again be paying just to store the car. Florence definitely needs more than 1.5 days.
Tha Amalfi Coast is another place where a car is less than useful. The beaches there aren't that great, but the towns and landscape are beautiful and interesting. April is kind of iffy for beaches, anyway.

Varenna is very easy to reach by rail from Milan, and a car is unnecessary at Lake Como.
The only place on your trip a car would be useful is while "doing Tuscany". ( Pick up car when leaving Florence)

All of your other destinations are easily done by rail.

I would suggest to you to reconsider going to CT vs. Sorrento. It would make for less travel and the Amalfi Coast is going to be crowded just because it is the AC. The tweak I would make is to do 2 nights in CT and add a night to Rome.

You outline a busy but doable schedule

For those cities, a vehicle is just expensive, excess luggage and the potential for a surprise package about a year after you get home. Four nights is little long for Montepuliciano, drop at least one night add to Florence. Still a lot of travel. Two nights stands especially with driving will limit the amount of time in each location to about a day.

Less destinations always has proven more satisfactory to my idea of travel to Italy, but everyone is different. I agree that trains is a better idea for most of your potential destinations. I would not pick up the rental car until departing Florence and would skip Sorrento, although it is fabulous, and spread the nights amongst the other destinations. Save Sorrento and the Amalfi for another trip. Other posters are right, your present itinerary has too much moving between locations that will eat up precious time that should be spent enjoying Italy. Dropping the rental car off in Rome is a good idea. I do disagree with another poster that 4 nights in Montepulciano is too much time. But I adore Tuscany, and Montepulciano is a good base from which to explore. There is so much to see and do in Tuscany, many little towns off the beaten path tourist path have much to offer. Well known towns such as Pienza, Cortona, Montalcino, montereggioni, Volterra, etc are very much worth the hype. You will definitely need a car in Tuscany. All my personal opinions, obviously.

For those cities, a vehicle is just expensive, excess luggage and the
potential for a surprise package about a year after you get home. Four
nights is little long for Montepuliciano, drop at least one night add
to Florence. Still a lot of travel. Two nights stands especially with
driving will limit the amount of time in each location to about a day.

I'd absolutely agree with biz-bagging the car with the exception of Montepuliciano (look at maybe cutting a night there?) and cutting Sorrento (too far out of the way) as well. Add nights to Venice, Florence and Varenna - 2 nights aren't enough to do any of those locations justice - and Rome could use another night as well as I consider 4 nights/3 full days the minimum for that one.

Are you aware the average temps for April at Lake Como for your time frame are H 60
L 50. You could also have significant rain. Think I'd skip it and add a night to Venice.

Train: Milano>Venezia>Firenze.
Rent car as you're leaving Florence to wander Tuscany.

A car will also get you to Sorrento quicker, add a day here and April is a halfway decent month to drive the Amalfi coast.
Turn in your car either in Sorrento, or drive to Naples airport to drop it then take the Alibus (15 min) to Napoli centrale and train to Rome.

Edit. Fly multi city, into Venice out of Rome.

Yeah, a car is only useful to tootle around Tuscany and maybe on the Amalfi coast. For the rest, it will slow you down. I'm assuming you are flying Milan/Rome because of non-stop flights, so other airports are not currently in the equation.

3 2-nighters in a row at the beginning of a trip can be very tiring and make the rest of the trip hard. I'd drop the lake idea and spend 3 nights each in Venice and Florence. You'll land at Milan Linate, then take the bus to Milan Central train station and then a comfortable fast train to Venice. Consider going first to Montepulciano, then dropping the car in Florence. I think you'll have better train connections to the Amalfi coast from there. Also consider staying in Salerno instead of Sorrento. It's at least as easy to access the coastal towns from there and it's connected by high-speed train to Florence and Rome.

Lastly, take into account that you'll use 1/2 day for travel each time you change locations. 2 nights in a place gives you 1 full day. You'll have a half-day on the 13th (after being in transit for a long long time). That leaves you 16 days. 4 of those are travel days if you drop the lake destination. That's 12 days to divide among 5 places.