I'm going to echo what other people have said about the long (!) travel time from Rome to Assisi. Plus, frankly, my strong advice is to skip it. While I'm glad other visitors have enjoyed Assisi, we found that it's overly filled with shops and stands selling junk to tourists. Almost felt sacrilious, a lot of it, particularly down around the Basilica.
If you someday want to visit a place with a more sacred depth to it, visit the peaceful sanctuary of La Verna, a profoundly silent mountaineous site St. Francis himself used as a spiritual retreat. But that's more if a person has time for a leisurely visit to Umbria, which my wife and I hope to visit for the month of June while you guys are on your trip.
Your kids will love Rome - particularly if you go on a gelato hunt every day. You get two flavors in one cone - it's sort of a tradition. Both our daughters, now with children of their own, still talk about having the best ice cream of their teenage lives every day for a week in Rome.
Also, after a family visit to Rome three years ago, my daughters and their husbands raved about e-bikes you can rent as part of tours on the ancient Appian Way, a two thousand-year-old superhighway paved in stone. A lot of fun for kids, and an e-bike tour for everyone in your group will be affordable if you skip the expedition to Assisi. The Appian Way is where Romans themselves nowadays head for a Sunday afternoon picnic in the countryside. E-bikes out there are the way to go. My grandsons also told me that the acqueduct that runs along the Appian Way was awesome, and they got very excited about the flock of sheep that blocked the road for a couple minutes.
Like other people have said, the broad and beautiful sandy beaches of Florida are completely diffrerent from the rocky Amalfi coast. Terraces filled with olive and lemon trees climb up the hills. Great walking opportunities. But Sorrento is the better site for a "base" rather than Positano or Amalfi itself. From the gentle town of Sorrento, you can do easy trips to the Blue Grotto, Capri, and Pompeii.
You're spending a kinda long time down there, and may want to give more of Rome a chance. It has a great zoo (that's now a BioPark), if your kids like animals, and if you are plant lovers, check out the Botanical Gardens behind the Vatican. As far as food goes, the pasta anywhere in Rome is to die for. Spaghetti alla Carbonara like nowhere else. Be sure to check out long-stemmed marinated artichokes - a local speciality.
