Welcome aboard, Peggy!
My favorite adventure in Naples for families with young children is
Pompeii, Sorrento and Capri For Families. I love that guests get to enjoy three beautiful spots in this port, all on one tour. That may seem like a lot with little ones, but this adventure is tailored just to families like yours, so your kids will have others their age to interact with, and the pace is a bit slower to accommodate the kids. But, you won't be sacrificing any sights or learning opportunities for yourself, since there is so much to explore.
In each port, Disney Cruise Line provides the kiddos with Port Activity Guides so they have something fun and educational relating to that exact port to keep them busy on the drives. That adventure, though includes boat rides as well as motorcoaches, so they are sure to be engaged the whole time!
I love Rome, so I couldn't possibly recommend one over the other there. It really depends on your particular interest. Personally, I'd spend the whole time at the Vatican, but there are also so many exciting options to visit the rest of Rome, especially if it's your first time there. Best of Rome is a great introduction, but check out the others offered there. Click on ages 3-4 in the side bar on the left to narrow it to only those that your kids can enjoy too.
I don't think a stop in the port of La Spezia is complete without a visit to Pisa to see the famous Leaning Tower. Now, if you've already done that, go ahead and choose a different adventure, but if it's your first visit, you can't miss this! The kids will think it's cool to pose for a picture pretending to hold up the tower and you'll enjoy Florence and Pisa's culture and history.
I'm about out of room, but stop back if you have other questions as you plan, Peggy!