Anita, I'm going to link one of your previous threads that may be helpful to responders:
https://community.ricksteves.com/travel-forum/italy/best-tours-for-sightseeing
The fact that you'll be moving 10-12 people around - and from a villa which likely requires either vehicle rentals or drivers - is significant as advance ticketing is almost a necessity at some attractions to avoid long lines. Also this:
My family and are will be going to Italy in June for 10 days. We will
spend the first 2 days in Rome....
If those 2 days/2 nights include arrival day, you only have one FULL day to spend in Rome. Arrival days are always partials, and often jet-lagged fogs at that so getting 10-12 people settled in a foreign city will likely be all that can be accomplished on that day. What to see/do in one FULL day depends on the make-up of your group: ages, interests and any mobility challenges taken into consideration. Young children and/or seniors who can only spend so much time of their feet will limit how much ground you can cover, and ANY group is only going to move as fast as the slowest member.
The #1 and #2 most-visited attractions in Rome are the Colosseum and the Vatican Museums. Advance tickets are a necessity to avoid long ticket lines, and one or both of them will involve booking a specific entry times. Both of these attractions will also be mobbed so doing them both in 1 day would be exhausting for even the heartiest traveler, even with a comprehensive tour.
Must-do attractions in Florence depend on what one is interested in. How many day trips are you planning into Florence, and are you planning on everyone doing everything together? Same as Rome, the several top attractions - the Uffizi, for instance - require advanced, time-entry booking to avoid the longest lines. Then again, if one doesn't care for art museums then it's not a must-see. Same for the Vatican Museums in Rome.
Long story short, it's less about what anyone else thinks is a cannot-miss but what's the best fit for your group, their interests and abilities. What can you tell us about the makeup of yours and their interests, and are you expecting to make a sightseeing itinerary just for YOU or for everyone?
possibly one more day at the end in Rome.
If you are flying both in and out of Rome then yes, you'll want to spend the night before departure in Rome. In fact, it would be more efficient to go directly to the villa near Florence on arrival day and put all of the time in Rome (3 nights/2.5 days) at the end of the trip.