Laura, I was going to be a Laura too, but came out a Lawrence, back in the day when no one knew in advance!
A couple thoughts from my experience in the area, a few years ago:
The best “splurge” of my trip in Italy was taking a taxi from Naples to Sorrento, door-to-door from lodging to lodging. And I was just one person, makes much more sense for a family. Took just over an hour, cost about 100 euros at that time. Was a very relaxing trip, eliminated all shlepping of baggage, making connections, etc. Remember, if you travel by train, you also have the time, hassle and expense of traveling between your lodging and train station, at both ends of the trip.
I would take the trip to Pompeii on a separate day, either from Naples or Sorrento, 30 or 40 minutes train ride from either city, without baggage. There are experienced, knowledgeable and affordable guides available around the entrance to the ruins, you can “interview” a couple or more, to choose one you like and can easily understand their English.
If you are traveling in the summer, try not to be at the ruins during the mid-day heat, it can be very hot, with virtually no shade. Try to arrive first thing in the morning, cooler and less crowded.
I can enthusiastically recommend a paperback tourism book about Pompeii to you. Unfortunately I bought this in the shop in the train station as I left Pompeii, wish I had had it during my visit to the ruins. It contains a lot of information and current photos of many of the structures and spaces in the ruins, but importantly also includes artist renditions of what the major structures and places actually looked like back 2000 years ago, with people using them etc. Really brings the ruins into focus. It is called “Pompeii — 2000 years ago and today” by Bonechi Edizioni “Il Turismo”. It cost 12 euros when I bought it, some years ago. Don’t know if you can find it in the US, but certainly in Naples, Sorrento or Pompeii.
Finally, be sure to visit the Archeology Museum in Naples, which is where most the art from Pompeii is located, mosaics, sculptures, etc.
Enjoy your wonderful family trip to Italy!