Overwhelmed with choices

"There will be four of us, me and my two daughters and one boyfriend (all in mid 20's---them, not me!)"

Your entire question about being overwhelmed seemed to be about you "I" I didn't see one "we" about your trip and plans..

Just curious if you are paying for everyone, and therefore just going to give them your itinary to follow with out any input from them?

You are travelling with 3 people in their 20s who must have their own tastes, interests and reseach capabilities.
Have you involved them at all ?

It just might be that they have other interests than you do - or do your plans (and theirs) mean you are doing everything together?
Are you all shairing a room? I understand that 2 are your daughers, but my guess is that the one with the boyfriend might want some time to explore on their own, or the 3 of them. You also might have intersts other than theirs, and they might also enjoy going out at night and exploring night life.

Since you have over 3 months, why not involve them in the planning. Maybe even split the days and give your daughers and the boyfriend some responsibilities in coming up with activities for 2 days each.

it might be more fun for them and you to contribute to this trip. Just saying.

I'm sorry, however your itinerary just doesn't flow well. Your time might be better spent going in one direction to cities that compliment each other.
Naples is about 150 miles south of Rome, and the Amalfi Coast is beyond that. Capri is off the coast at Naples.

Tuscany is where Florence is, and it's 170 miles north of Rome. To get to Lucca, most ride the train an hour west of Florence to Pisa and then go north by train to Lucca.
If you want to see Lucca, you'd do better to substitute the Cinque Terre in place of the Amalfi Coast.

Many travelers will travel to Tuscany, stay in a central location and do day trips into the countryside to see the hilltowns. Many stay in Florence and many will stay on agriturismos south of Florence 30-45 minutes away. Unfortunately, the time allotted will not allow you to cover that large of an area and still find time to relax.
You really should go back to the drawing boards. Why don't you get the "kids" into figuring out the trip as they outnumber you. Florence and Rome are both too important of cities to avoid or limit to visiting for only one day.

We didn't quite have enough time to do Tuscany justice on our trip, but found that a good substitute was to take a full-day tour of Tuscany so that we could at least get a taste of the area. If you find that your trip ends up getting too full (packing in too many things will make your trip stressful), that could be an option. We loved the Walkabout Florence Best of Tuscany tour, which included lunch at a vineyard in Chanti as well as stops in Siena, San Gimignano, and Pisa for a decent price. There may be other similar tours out of the cities you'll be in, perhaps one that includes Lucca.

You are wise to limit yourself in number of locations since you only have 8 nights. It would be best to stick to two locations: Either Tuscany and Rome or the Amalfi Coast and Rome. Either combo is feasible without a car.

Sounds like you are really drawn to the Amalfi Coast (and maybe less so to Rome?) so I will address my comments to that as an itinerary.

• Arrive Rome and transfer to Sorrento. You can take a high-speed train from Rome to Naples and then the Circumvesuviana train, but with 4 of you, a private transfer might make sense. Spend 5 nights. Allocate one day to Capri, one day to a bus trip down to Amalfi Town, and one day for Pompeii, and one day for hanging out in Sorrento. Go to Pompeii EARLY in the morning to beat the heat.

• Transfer to Rome EARLY after your five nights in Sorrento. Drop your bags and head out to see the sights. Try to arrive in time to have lunch in Rome, then take a nice orientation walk like Rick Steves' has in his Rome guide (Caesar Shuffle, Dolce Vita Stroll, etc.). Then allocate a day to ancient Rome (Colosseo, Palatine Hill, Forum) and your final day to whatever interests your group: Vatican, Borghese Gallery, shopping, traipsing through Trastevere, etc. 3 nights Rome.

I think Laurel has it right.

You are too spread out with your wishes. Laurel's plan for Naples/Amalfi is a good one. You won't find trains on the coast but there are buses. You can drive but buses are less stressful.

Give up Tuscany this trip and enjoy Rome. To maximize your experience hire a guide in Rome. You can see a lot in a day with a guide and maximize the highlights. Be sure to give yourself your own time too. Do a dinner in Piazza Navona as a last dinner in Italy.

Thank you everyone for your thoughts and suggestions. I really appreciate your willingness to share your experiences and knowledge. I suppose I should have mentioned that I have been to Italy before and have experienced the highlights of Rome, Florence, Venice, Assisi and Pisa, although it was a long time ago. This is my "bucket list" trip and when the kids found out my intentions, they were more than willing to tag along. There was only one request to see Rome, and that is why I would like to arrive in Rome that Friday night so that we would have all day Saturday to see just a couple of attractions, knowing that there will be crowds and such. I know this sounds very selfish and mean, but believe me, they are not complaining. God willing, they will have the opportunity to return some day and do the trip they would like to do.

I will go back to the drawing board and try not to get too many apples in my basket, but my goal is to still try to see the Amalfi Coast and Tuscany. I'll just have to be more realistic about what can be squeezed in.

Thanks again!

Sorrento makes a good home base when using public transport - commuter train to/from Naples, Amalfi coast bus, and ferries. That probably also makes it easier for people in your party to go different directions, if they wish. If you want to see Naples' Archeology museum on the way into or out of the area, you can store luggage at Napoli Centrale train station; or it's possible to day-trip back by train without your luggage.

Maybe you're feeling in need of a relaxing vacation. But there is a lot to see in Italy that you can't see at home, which is why Rick and company tend toward a more intense sightseeing schedule. On one day out of 7, we suggest a more relaxed "vacation from your vacation." A fairly full schedule does not have to be inflexible nor necessitate everyone doing the same thing.

From Naples to Lucca by train takes 4.5-5 hours with a connection in Florence. See www.trenitalia.com or the DB link at How to Look Up Train Schedules and Routes Online. You can pick up a car in Lucca later, when you're ready to drive. Or, if you wanted to go to Montepulciano first, you can take a train to Chuisi and pick up a car near the train station. I'm not saying whether you have time for all of this, but the train connection should not be a "main concern."

P.S. I see after writing this that it's not your first trip to Italy. Apologies if my editing has sent you several emails.

If you also want to see Pompeii, you will need at least the 4 nights for the Amalfi Coast.
I would skip Naples.

Priano is served by regular buses. They are cheap and convenient. The issue with them can be they fill up and since Priano is a middle stop, buses are unlikely to drop enough off in Priano for your party to board so you may end up waiting for the 2nd or 3rd bus before you can board.
Convenience wise staying in Sorrento, Positano or Amalfi is better.
I think the rest of your party would greatly prefer Sorrento or Positano, Priano may be too sleepy for them.
You can catch a ferry to see Capri for a day trip from either Sorrento or Positano though if the waves are strong they would cancel the Positano ferry well before the Sorrento one. I don't think there is a boat that goes from Amalfi to Capri but could be wrong.

If you decide to go up to Tuscany, why Lucca? I wouldn't go that far, if wine is of interest stay 2 nights in Montepulciano which is much closer than Lucca as the surrounding countryside scenery outside of the town is going to be far prettier.
Most famous photos you have seen in books and online of "Tuscany" are taken in a very small area near San Quirico which is an easy drive from Montepulciano.
You could also look at the towns of Montalcino and Pienza in that same immediate area.
If going to this area a car works well, cars don't work well at all for Florence or Lucca, these smaller towns though are better with a car. I would likely rent the car from Orvieto, which you can reach by train and then have about a 90 minute easy drive to the towns above.

Sounds like you have been to Florence and further north in Tuscany so these towns south of Tuscany could be perfect for you.
You can even return the car to the same rental place in Orvieto and easily catch the train back to Rome. May even want to allocate a good portion of that day to Orvieto itself.