Which city should we drop?

I would go crazy after 2 days in Venice.

You might find the weather in the CT in March to be a bit dicey. If you spend more time in Tuscany, you could make it an optional day or overnight excursion once you have a bead on the weather.
Edit: I can't get enough of Venice, so to each his own.

I like Venice, but in March I think I would drop 1 day there and add it to Tuscany. I also think CT weather could be dicey so might think about taking 1 of those days and adding it to Rome. But it could be glorious weather so who knows.

I prefer to count nights on the ground rather than days.
Consider that 3 nights in a place is only 2 full days plus a few hours on the day of arrival.
Assuming an arrival on the ground on March 10 and a departure on March 28, that is 18 nights. If you actually depart on March 10, you will arrive on March 11, therefore it would be 17 nights.

This is my personal allocation for 17 nights, but to each his own:

Arrive to Venice (VCE) airport
Venice= 3 nights (2 full days) is the minimum for the city + the islands (Murano and Burano and Torcello).
Cinque Terre= 2 nights (you might want to cancel this and do it as a day trip from Florence depending on weather in March)
Florence=5 nights (1 or 2 days for Florence, the rest day trips in Tuscany)
Assisi= 3 nights (one day Assisi, one day trip to Spello or Gubbio) a car would be useful but not essential.
Rome=4 nights (2 days Rome, 3rd day more Rome or Orvieto day trip)
Depart from Rome (FCO) airport

Regarding the Cinque Terre consider that March may be still rather cool. Also Europe switches to daylight savings only on the last Sunday of March, therefore during your stay, the sun goes down by 6:30pm.

We are:

Four nights Venice
Two nights Assisi
Four nights Florence
Three nights CT
Four nights Rome

Some people like Venice...others don't. It is my favourite place ever. I've been there 10 nights over 4 trips and could go and spend another week there (and hope to go back in a few years for Carnival). The best part of Venice is the back streets and canals - you can spend a day alone just doing Murano/Burano. Not sure how it would be in March tho - we've only been there in Sept.

I'm not sure how much would be going on in CT in March - usually cold/rainy and/or stuff shut down. If I was taking out 3 nights in CT I'd add a night to Rome and one night to Florence...or two nights to Florence and use one for a trip to CT weather permitting.

...but otherwise your night allocation looks pretty good!

Our first trip to Venice (on an on-our-own 2 week Italy trip) we only allowed 2 nights and both said afterwards we wished we would have spent an extra day in Venice. Three years later we went back to Venice prior to a RS Village Italy tour, stayed 4 nights and loved it. A perfect place to get over jet lag and to acclimate into the Italian culture. I think your time allocation is great except for Assisi. I really was looking forward to that stop but after visiting there I thought it was just a big tourist trap worth only a day visit. Enjoy your trip!

Your schedule looks good, although planning for CT in March is kind of iffy, due to the seasonal weather and the fact that many businesses will still be closed. Of course, you only need for one room and a couple of restaurants to meet your basic needs there. I think four nights for Venice sounds good. Your arrival day will likely be low key due to jet lag, and there are plenty of day trips available, like Murano/Burano/Torcello, as well as Padova, Vicenza, etc. Lots to see and do in Venice, including just wandering around. Another wonderful stop you might consider between Florence and Rome is the Umbrian hill town of Orvieto, lots to see and do there, and some excellent food, wine and crafts, easily reached by train from Florence, then just 70 minutes on to Rome.

Roberto's suggestions sound good. Since you said you want to stay in a villa outside of the main cities (I am assuming Tuscany) you might want to give up CT this trip and divide the time between Florence and an outside villa.

We absolutely love Venice and are returning to it again this year. But, we're there when it's warm and are spending almost all of our time outdoors. For March, I would drop a day of Venice and a day of Assisi and stay two days in Siena.

I've been to Venice twice in February and it was lovely to be outside though I did get a couple rainy days. I'd go with 4 nights Venice. If you really aren't enjoying yourselves, you can spend a day in Verona and a day in Padua easily enough. Keep in mind that ending in Rome puts you there for Easter weekend and huge, huge crowds. It's good if you want to be in Rome for Easter, not so good if you are planning on lots of sightseeing.

Four nights Venice
Two nights Assisi
Four nights Florence
Three nights CT
Four nights Rome

Our first trip here in 2010 we spent 4 nights in Venice (Venezia in Italian) and it was a perfect amount of time. Since then we've spent another 25 nights-or-so and never tire of it. WE'll be back again March 21. :-)

I love the CT in fall, but I think March is early. I would eliminate that stop and add a night each to Assisi and Roma. Roma has endless things to fascinate. Again, we did 5 nights our first trip and it was perfect. Now we live here are we still aren't "done."

In Umbria, Assisi makes a good base and you can go a lot of places by train and bus. Perugia, Spoleto, Spello (so cute!).

The Tuscan villa experience is, IMHO, much better in more dependable weather. We stayed at an agriturismo last February that in April-October would have been great, but the heating could not keep those stone walls warm in the colder weather and we slept in our sweatpants and fleece tops. Stick to cities and towns -- and hotels or apartments -- at this time of year.

Consider an escorted wine/countryside tour in both Firenze (Florence) and Assisi. WE like Tours by Roberto and Gusto Wine Tours.

Forgot to add: You'll want to make your high-speed train reservations as soon as you pin this down. There are still discounted fares available, but they disappear!