All you can do is check the historical weather records and decide for yourself. For me, the Amalfi Coast, Lake Como and the Cinque Terre would not be on my itinerary for a late March, early April trip. But that's me. IMO, your bigger problem is that 9 destinations in 15 days is 4-5 too many destinations, esp. considering the travel distances/times involved. (FYI, the train ride from Malpensa to Naples on your arrival day is more than 6 hours. One day down already.) In March, sunset will be about 6:30 p.m., but because of the time change sunset in April will be closer to 8:00 p.m.

http://www.weatherbase.com/weather/city.php3?c=IT&refer=&name=Italy

I'm OK with Amalfi Coast and some other parts of Italy in April, but probably not Cinque Terre or Como. I think you could cut out those two destinations and make the trip a bit more doable. Including those two involves a lot of travel time (and even dropping them still involves a lot of travel time.

So, now you're talking about Milan, Venice, Florence, Siena Rome, Naples and the Amalfi Coast. Seven destinations in 15 days, with travel time in between. Whew!

March is a period of very unstable weather throughout Italy. If you can go in April, it is better -- but that is still springtime, and you can get quite a bit of rain, enough to impede travel if you are driving, or to make some scenic destinations pretty dreary.

If you are traveling with an internet connection, you can watch the weather forecasts (and should) to avoid places that are pointless to go to in the rain or that are experiencing problems related to too much rain.

With 15 days, you should try to limit your trip to 4 or 5 desstinations. I would do no more than 4 but you seem to want to do a lot in a short time.

I would go as late in April as possible to get the best shot at decent weather and avoid Cinque Terre at that time.

If you haven't already made your plane reservations, book and open jaw (or multicity)flight, into your first city and home from your last. It shouldn't cost more and will save you time.

Crazy scheule; the weather is the least of your considerations. Cut down on the destinations. As far as weather is concerned, use the internet to forecast it.

In your time I wold do 3 or a tmost 4 hotels - so you don;t spend all that time and money on a tour of the train stations of europe.

Late April is better and May better still, March weather can be very uneven quite rainy and chilly (not sure where you are from or what weather you are used to then - where I live you can still get substantial snow).

I definitely would not do Como or CT at that time. At end March a lot of places probably won;t be open for the season yet - and outdoor activities may not e very pleasant.

I've spent a total of more than two months over several trips, in Rome and south, Naples, Amalfi Coast, etc, in April, and for the most part had warm, sunny days, a few cloudy and drizzly, and one stupendous storm with thunder and lightening. Not swimsuit weather, but pleasant for sitting outdoors at lunchtime. Evenings cool, which wasn't great because the places I stayed all turned off their heat April 1. B-r-r-r-r, very chilly mornings, had to jump into the shower first thing to warm up before breakfast!

As others advise, I'd avoid the Lakes up north and CT, unless you're there toward the end of April or beginning of May.

And why not look into flying into and out of Rome? From Rome you can go south toward Bay of Naples/Amalfi Coast for a few days, then drive north, exploring some of Lazio, take a swing into Umbria, maybe up to Siena and Florence, following a different route back to Rome to fly out.

There are many pretty, interesting, 'hidden' places between Rome and Siena. I could give you more info if you're interested. Milan doesn't make much sense to me unless you're going to the Lakes.