Two week trip to Italy

I assume you have flights booked? If so, where to/from? That will help shape suggestions for an itinerary.

Yes...arriving in Rome, departing from Milan.

Orvieto, Siena, and Varenna (or elsewhere on Lake Como) spring to mind.

What are your kids interests? Let them help choose places, show them videos or books.
I like Lucca, you can walk or ride bikes on the wall. If you want to stay there, stay inside the wall.

One possibility is:
May 30 - fly
May 31 - arrive Rome
June 1 - Rome
June 2 - Rome
June 3 - Rome/Day trip to Orvieto
June 4 - AM train to Florence
June 5 - Florence
June 6 - Day trip to Siena/Tuscany tour
June 7 - Florence
June 8 - AM train to Venice
June 9 - Venice
June 10 - Venice
June 11 - AM train to Varenna/Lake Como
June 12 - Varenna/Lake Como
June 13 - AM train to Milan
June 14 - fly home from Milan

You can adjust days in each location to suit your tastes. The isn't much time in Milan on this itinerary so you may want to take a day from another location and add it here.

Places to stay: Suggest apartments using VRBO.com, Homeaway.com or AirBnB. This will provide more space for the family and is usually a better value than hotels.

Thank you all for the suggestions! Stephen, I appreciate the detailed itinerary suggestion. Have you done this before or one similar? I’m just wondering how ambitious it is or if it’s reasonable for a group of four? Our children have traveled extensively and do enjoy hiking, biking as well as museums and architecture.
Thanks!

I have done similar trips 3 times! Two of those times there were 4 of us and just two of us on the other trip. We once went from Rome > Cinque Terre > Florence > Venice. I don't think this overly ambitious and it gives you and your husband a chance to see things you haven't had the chance to do yet. At that time of year, you will have plenty of daylight. Just be sure to check opening/closing times for places you want to visit. you can get train ticket in advance for a reduced rate if you know your travel dates and preferred travel times. Check trenitalia.com and italotreno.it. Both companies offer high speed trains between Roma > Firenze SMN, Firenze SMN > Venezia S. Lucia, Venezia S. Lucia > Milano Centrale. Trains from Rome to Orvieto can be purchased at the station day of travel.

Edit: My suggestion has limited time in Varenna and Milan. You may want to take a day from Venice and add it there or make Lake Como a day trip from Milan to avoid changing hotels one more time. I would also make sure the kids have a chance to pick some activities along the way.

I've read that there are lots of beautiful hiking trails around Lake Como, so that sounds good for your family.

A variation on what Stephen proposed ..

May 31 - arrive Rome (3N)
June 1 - Rome
June 2 - Rome
June 3 - AM train to Vernazza/CT (2N)
June 4 - Cinque Terre
June 5 - Train via stop in Pisa to Siena (2N)
June 6 - Siena
June 7 - Train via stop in Florence to Bologna (2N)
June 8 - Day trip to ?? (Ravenna, Parma, Modena, Ferrara)
June 9 - AM train to Venice (2N)
June 10 - Venice
June 11 - AM train to Varenna/Lake Como (2N)
June 12 - Varenna/Lake Como
June 13 - AM train to Milan (1N)
June 14 - depart Milan

A further option to play around with ...

May 31 - arrive Rome (3N)
June 1 - Rome
June 2 - Rome
June 3 - AM train to Vernazza/CT (2N)
June 4 - Cinque Terre
June 5 - Train via stop in Pisa to Siena (3N)
June 6 - Siena
June 7 - Day trip to Florence by bus
June 8 - Train via stop in Bologna to Padua (3N)
June 9 - Padua
June 10 - Day trip to Venice
June 11 - AM train to Varenna/Lake Como (2N)
June 12 - Varenna/Lake Como
June 13 - AM train to Milan (1N)
June 14 - depart Milan

When we went in 2015, we did:

Venice (3)
Florence (3)
Siena (2)
Cinque Terre (2)
Rome (4)

We thought this was a nice itinerary. Wish I had more time in Siena/Tuscany.

We stayed in Vernazza in the CT and thought it was excellent.

Verona is a short way from Venice and makes a good day trip or a couple of days.

Ok, we have it narrowed down. Now, trying to figure out the best path. Is there a preference of the order between the following two itineraries?

Rome-Siena/Florence-CT-Verona/Venice-Milan

OR

Rome-CT-Siena/Florence-Verona/Venice-Milan

OR

Rome-Siena/Florence-Verona/Venice-CT-Milan

It’s probably easiest to just remove Venice altogether but our children really want to visit Venice.

Thank you all so much!
Tanya

If possible, try to fly into Venice and out of your last city. Makes the logistics much easier. I'd opt for Venice with a day trip to Verona (4 nights), Florence (three nights), and then Rome (4 nights). That still leaves a couple or three days for spur of the moment things such as day trips.

Our flights are already set...flying into Rome and out of Milan. Unfortunately for the dates I was looking, I could not find great options for flying into Venice.

That being the case, I'd go for: Rome, Florence (day trip to Siena), Verona, Venice and finish up in Milan. Verona can be done as a day trip from Venice or as a stop over between Florence and Venice or as an overnighter. Enjoy!