Hi Heather -
I'm piling on with the rest of the folks: you have way too much for way too little time. As far as how much time you accurately have to work with, how many NIGHTS will you have ON THE GROUND in Italy? 10 nights in the country is different animal than 10 days of travel which could include arrival day, which is always a partial, and a travel day home.
Can I do a "for instance" itinerary with a guesstimate number of days? Skipping Milan entirely - as you don't have any interest in seeing it anyway - and flying into Venice...
Overnight flight to Venice
Day #1 - Venice (this is a partial day and could be a jet-lagged one). Sleep Venice
Day #2 - Venice
Day #3 - Transfer by train to Florence (partial day)
Day #4 - Florence
Day #5 - Florence - day trip by trains to Lucca and Pisa
Day #6 - Florence
Day #7 - Transfer by train to Rome/partial day)
Day #8 - Rome
Day # 9 - Rome - day trip to Ostia Antica
Day #10 - Rome
Day #11 - fly home from Rome
You see that I've eliminated some locations and trimmed the entire thing down to just Italy's "Holy Trinity":: Venice, Florence and Rome. While you've already been, the other 3 of traveling companions have not, and moving 4 people from accommodation-to- accommodation eats time so it's often more efficient to unpack ONCE and just day trip, where possible. Florence is a really good base for any number of those so if you think the 2.5 days I've allotted to explore that one is too much for your family, add another day trip (by bus) to Siena.
As well, longer stays make apartments more comfortable/economical choices than hotels when traveling with a group. With 4 people, you might enjoy the sort of space apartments can offer plus the bonus of a kitchen for leisurely breakfasts in your PJs.
I've substituted Ostia Antica for Pompeii as the latter is a really brutal day from Rome unless willing to take it on independently by rail. Practically all of the escorted day trips from Rome are by bus, and involve 6+ hours of sitting on the things: no fun for teens/pre-teens. A good chunk of that time can be shaved by taking a fast train to Naples (not inexpensive if buying day-of tickets) + commuter train to the scavi. That said, Ostia Antica is much, much closer to Rome, and can be reached by very inexpensive local train. Save Pompeii for a future trip that includes Naples (especially the archeological museum where many treasures from the excavation are housed) and more of the Sorrentine/Amalfi Coasts.
Cinque Terre: I've taken that one out too. It CAN be done as a long day trip from Florence but I don't recommend it. If the trajectory of numbers continues to track upwards, the CT could be positively heaving with visitors, many of them daytrippers, next August. That one deserves 2 nights - time you don't really have - and is weather dependent as far as hiking the trails 'cuz they usually close those when it rains. If determined to do it as a day trip, let us know as there are two trains - one from Florence and another one back to the city - that cover ground in the shortest amount of time: just under two hours to/from La Spezia + additional time for short train rides to the any of the 5 villages from there.
Rome: LOTS to see there so I wouldn't cut allotted time any shorter than I already have!
If you can add days, so much the better as Venice could use another one, and maybe you could add 1 night in Orvietto on the way to Rome (as much as I don't recommend 1-nighters.)
Some stuff to think about? :O)