Best place to make a base in Tuscany

A warm welcome to the forum, Liz!

Right off the bat, I think you'll hear from a lot of the posters here that your itinerary is too ambitious, and that Rome and the A.C. both take more than 2 nights/1 full day to both acclimate to the surroundings and to adequately sightsee. I also have an issue with just 1 partial day for Florence, depending on your group's interests.

You definitely do not have time for Venice, and with just 9 nights/8 full sightseeing days to work with, I would cut the Amalfi Coast - it's your outlier - and would not add another location: do just Rome, rural Tuscany and Florence. Alternately, you could do Venice, rural Tuscany and Florence, or Venice, rural Tuscany and Rome. In all cases I'd fly into the first city and out of the last one. This is still pretty aggressive; I consider 4 nights/3 FULL days the minimum for Rome.

staying in a Villa for 4 nights about 40 min west of Tuscany, 15 min outside of Lucca.

Not sure what this means? It sounds like you have a particular property in mind?

The car: as you'd be first-timers to The Boot, be sure to do the homework regarding the in and outs of driving in Italy. Also be aware that all drivers will need International Drivers Permits, and that you may need 2 cars to accommodate 8 adults and their luggage. (Dunno, maybe a large van might be able to work but will need input from others on that topic). There's also caution about leaving anything at all of value - like your luggage - within view while away from the vehicle so sightseeing en route from accommodation to accommodation can be a little risky.

Consider as well that unless the villa offers meals and you're OK eating at the same place every night, just going to dinner will likely involve getting behind the wheel: be aware that Italian drink-driving laws are even stricter than the States.

Although you'll likely have multiple vehicles, a rural accommodation can limit all of you to doing everything together unless some are just happy to remain at the villa and/or others are comfortable enough to drive off on their own. As there's already some contention regarding the A.C. versus Venice, more urban bases w/public transit to locations both inside and to points outside of the city can allow couples some easier, individual sightseeing according to their interests. For instance, some may want to see more of the museums in city __ whilst others would rather take a wine or food tour. Not trying to do EVERYTHING together can eliminate some potential too-much-togetherness and friction down the road, especially if you 8 have never traveled together before, and especially if the others are not actively researching/adding to the planning of this trip as well. A central location can also accommodate both late sleepers and their companions who are up and rarin' to go at dawn (that would be my DH and I). Otherwise, your group, as a group, is only going to move at the pace of the slowest member. 😉

Just a couple other recent threads where where the pitfalls of overloaded itineraries are addressed and why those can be an issue...mostly because there's NO flex for anything at all to go awry, too much packing/unpacking/checking in/out, time spent in transit versus enjoying the sights, and stressful sightseeing at a dead run.

https://community.ricksteves.com/travel-forum/italy/flying-in-out-of-rome-need-help-with-10-day-itineray

https://community.ricksteves.com/travel-forum/italy/venice-florence-rome-almafi-trip

There are many wineries in all Tuscany.
What kind of wineries do you want to see? Just a normal winery with grape picking, pressing grapes, trying various wines done on the spot or also have a whole dinner with special dishes associated with specific wines.

Lucca is a wonderful place to visit but is too far west to be used as a hub for visiting much of Tuscany. Siena or nearby would be preferable to see what you want to see in Tuscany.
You do not have near enough time to make your itinerary work. Cut it back.
No, you can’t visit Venice asa day trip. Rome needs more time. With only nine days, Rome and Tuscany, which includes Florence, would work for your group. Most Tuscan villa rentals are for a one week minimum.

Consider the idea of staying for 5 or 6 nights in a big enough apartment or house in Siena (there are a number of these --- I just looked), within the old city walls or just barely outside them but still up on the top of Siena's hill, and within walking distance to one of Siena's parking lots where you would keep your two rental cars or your 9-passenger van. You could, for instance, fly into Florence, spending a night there if you want to, rent your car(s), and drive to Siena. Fly out of Rome after spending a couple nights there. Or spend your entire trip in Tuscany and just skip Rome for this trip. Siena, Florence, and day trips can easily take up all the time that you have, even if you do not step into a single art gallery or church.

Staying in a town will give your large group far more independence and more possibilities to split up and do different things. You do not want to be the (unpaid and learning-on-the-job) tour leader keeping this whole group together and transporting them around.

Good comments from the others - particularly Kathy whose advice I'd take to heart.
You don't have enough time to visit all of the places on your proposed itinerary, and trying to do so is a recipe for disappointment. With the challenges involved in moving 4 couples around you're best advised to stick to a couple of cities and forget the idea of a car this trip - just way too complicated. My suggestion is to concentrate on Rome and Florence as bases. Your first day (or two) in Rome will be a jet-lagged and sleep-deprived blur, so I wouldn't plan on a terribly active or ambitious pace the first couple of days there.
The advantage of basing in Rome & Florence for your group is that it opens up the possibility of day trips outside the city for those who'd like to pursue their own specific interests for a day, with the option of meeting back up for dinner in the evening to swap stories and experiences.
From Florence, for example, there are easy day trips by train to Lucca, Pisa, and Siena ... all less than an hour and a half away. No need to book a tour for any of those unless you particularly want to. Booking trains in Italy is pretty easy and straightforward, and organizing your own day can be an enjoyable memory for your first trip - am thinking in particular about renting bikes and exploring Lucca.
A day trip to Venice from Florence actually is an option - though it would be a long day and require an early start. It's about 2+15 each way from Florence, for info, which means you could catch an early train and be in Venice before lunch with plenty of time to wander the city, catch a water taxi, ride a gondola, and generally get a taste of the city's charms before your return journey. We've found that the return trip is ready made to order for a nap on the way back.
Best advice is to slow it down and take it easy on your first visit, particularly with a group as large as yours. Safe travels.

We always make our base in Lucca. It's a beautiful city and has more charm than Siena. From Lucca, we do easy day trips to Florence, Pisa, Siena, Volterra, Viareggio & Forte dei Marmi, San Gimignano, and my favourite -- the Garfagnana.

Thank you all for your responses! It’s great to hear back! I am clearly hearing that my itinerary is too ambitious. I should add though, that this will likely be the ONLY trip to Italy that most or all of us will take so it’s hard to stick to just two areas. We are a gp of 4 sisters and our husbands and we have traveled somewhat extensively in the us and have recently traveled to Ireland. So we’re pretty good at traveling together. However, I do feel the pressure to include everyone’s top choices for sight-seeing if possible which is why this is difficult. My thought about staying in a villa and renting a car in Tuscany, is that it gives us the freedom to stop and see the small towns, etc, en route to the larger ones. And I think it would feel like we are really experiencing the Tuscany country side. We successfully rented a van and drove through Ireland last summer. It is also so much more affordable than staying in hotels. However I do wonder if it would be better to stay in Florence and travel by train from there allowing us to relax over dinner and be close to our accommodations. The villa, however offered the option of making a dinner for us and we hoped to include a cooking class with dinner one night in Tuscany as well. Drinking and driving won’t be an issue for us but I’m not sure about driving in tuscany after dark. My thoughts on amalfi were to take the train to Salerno, likely spend the night there and take a private tour along the coast the next day, spend the night in Salerno again, and next morning train to Florence. Not worth it? Also to Nickelini, can you give me some advice on what you like to do in the Garfagnana? Thank you all very much! I’ll look forward to your advise/thoughts!

My thoughts on amalfi were to take the train to Salerno, likely spend
the night there and take a private tour along the coast the next day,
spend the night in Salerno again, and next morning train to Florence.
Not worth it?

I will say no. For me, just one day for the coast is taking the risk that you're going to have sunny, wonderful weather. That may or may not happen: it poured buckets on us on the train from Rome to Naples and onward to the A.C. region but we had more time than you will so it wasn't a washout. What if the one day you allowed for this part of the trip is wet? Sightseeing the coast by boat or vehicle in the rain wouldn't be fun.

...renting a car in Tuscany, is that it gives us the freedom to stop
and see the small towns, etc, en route to the larger ones

That's fine. Just be aware that you can't drive into or park willynilly in all Tuscan towns (read up on ZTLs and whatnot if you haven't already done so) and you might want some detailed advice from those in the know for a vehicle in Siena. .

...that this will likely be the ONLY trip to Italy that most or all of
us will take so it’s hard to stick to just two areas

Think of it another way? The more to try to cram into a short time, the more you're going to miss: it's time, energy and $ eaten up in the transfer processes versus sightseeing. The more transfers you do, the more time, energy and $ consumed. With just one full day to give them, you're going to miss a lot of Rome, a lot of the A.C region and a lot of Florence. I guess I'd ask how you want to make best use of your time and travel budget?

I have taken your advice and we have cut back our trip by cutting out Amalfi. I now I would love advice on how to spend the last two nights of our trip. We have two nights in Rome, two nights in Florence, four nights in Tuscany (villa near Lucca) and are trying to decide how to spend the last two nights. Would it be best to go back to Rome making it a round-trip flight or spend two nights in either Cinque terre, Lake Como, or Venice, flying home out of Milan?