Italy in March

Rome, Tuscany and Venice work better than with Amalfi Coast. Or Rome, ( Naples, Capri) and Amalfi Coast.

I have been to Italy twice in March, most recently this past spring when I spent a few days in Venice. Both times the weather was pleasant , temps in the 50's and 60's and I just needed a light jacket. The main advantages are 1) it's not hot, and 2) it's not terribly crowded. I wouldn't hesitate to go again in early spring. My experience was limited to Rome and northern Italy; things might not be operational on the Amalfi coast.
Have fun.

With 12 nights, 11 full days (plus arrival day) you could add a third destination. If you've not purchased your plane tickets and decide on Venice, consider flying open-jaws into Venice and out of Rome. If you're already locked into a round trip to Rome, then consider going directly to either Venice or Amalfi Coast on your arrival day. Some will say no to that idea, but it won't be your most productive day so might as well use it traveling to your furthest destination. I would save Rome for the end of your trip if that's where you'll fly home from. Late March is a nice time to visit. It will be cool (not cold) and you may get some rain (usually not all-day rain), but crowds shouldn't be too bad. If your trip extends into early April, the free first Sundays at state-owned sights ends in March so don't plan on that.

Venice is easier to add to a Rome-Tuscany trip than Almafi because high speed trains take you right into Venice, but you can only get to Solerno or Sorrento and then you have to make bus or taxi connections. With 2w less travel time, if you want a coastal experience with a north-oriented itinerary, I would pair Rome-Tuscany and Cinque Terre instead of also going south. Don’t get me wrong, Almafi is wonderful, just more logistically complicated because of access. Cinque Terre is also isolated, but with trains!

We did Rome, Naples and the Amalfi Coast in March. The weather was very pleasant. Many places on Amalfi Coast were just opening for the season and it was nice to have it be not too crowded.

We've been to Italy twice in in March. I enjoy being there without the heat and crushing crowds. But with a fairly short trip, I'd plan on Rome + places further north OR Rome + places south. Trying to do both takes up a lot of travel time. If you opt for the AC, double. check to see if all the ferries will be running. It might be too early.

I've been to Italy in March a number of times. There is always a mix of nice weather (60s, 70s, even 80 and sunny) and not so nice (50s and rain). So cities and flexibility are keys. Cities (Rome, Venice, Milan and even smaller cities like Siena, Bologna, etc.) will have things to do if you do get crappy weather. I once spent several days in Sorrento in March and had a couple of glorious days with bright blue sky and warm temps and it was heavenly. Then it poured rain for a couple days and there is NOTHING to do in the rain. I could have gone up to Naples but had just done that recently. I ended up leaving a day early for Rome. When after the rain stopped it was again gorgeous. Another trip (different March) I had 'OK' weather in Venice and Florence but then the forecast for Lake Como, my next destination, was 3-4 days of solid rain. I changed my plans and went to Rome where it was sunny and 70.

So point is try to be at least a little flexible unless you plan to spend a lot of the time in the cities. In both the cases I mention, I had hotel reservations that could be changed until a couple days ahead so I was able to rearrange things. I did have to 'eat' a train reservation I had made in advance, and once I had to 'eat' one hotel night. But since prices are fairly low in March I figured it was worth it.

Another tip is to book yourself into cities and plan day trips. For example if you want to do Lake Como, base in Milan and do it as a day trip if you get good weather, on rainy days stay in the city and go to a museum. Not always ideal but good for destinations where you'd be miserable in the rain.

Here's my trip report from my most recent March trip - I even titled it "Chasing the Sun in Italy in March"
https://andiamo.zenfolio.com/blog/2017/5/italy-through-fresh-eyes---chashing-the-sun-in-italy-in-march