ESL - I echo the others in that, as a first trip to Europe, you're probably biting off a little much by wanting to visit Tuscany AND Paris AND London in 12 days.
I've spent a total of ~18 days in London and could still spend endless amounts of time there... I've spent ~40 days in Italy (Venice, Padua, Florence, & Rome), and feel like I have barely scratched the surface. That being said, please slow down and enjoy yourself.
About Europe in general and Italy in particular. I've driven in NYC and Philly and it's a WHOLE lot easier and simpler than in Italy. Urban Europeans don't drive much because the cost of owning, operating and parking a car is extremely expensive. Before deciding to rent a car in Italy, google "driving in Italy" and "Italian ZTLs". You might also want to search this forum for both subjects as well.
Tuscany is a region in Italy. Do you have something specifically you are trying to see/visit? As this is your first visit to Italy, I would recommend you make a major Tuscany city, like Florence, your base of operations and then use public transportation or escorted tours to see the Tuscan countryside. Fore instance, I easily visited Pisa and Lucca in one day using Italian rail from Florence. Plus, there are a ton of reasonably-priced hotels, B&Bs and holiday apartments in Florence. The old city is easily walkable (but un-drivable to non-residents and cab drivers) from the train/bus stations to any of the major tourist sites is only about a 15-20 minute walk.
The good news, most of Italy is saturated with very good public transportation. You can get from Florence to Rome or Venice in less than 2 1/2 hours by train. You can also get from Florence to most Tuscan hill towns fairly easily via public buses.
Flying into Italy from the USA will probably mean you will arrive in Rome (FCO), Milan (MXP) or Venice (VCE) if you want to fly non-stop. (The Venice non-stops by American are seasonal I think and may not be available in the winter...) However, most itineraries have you connecting in one of the other major European hubs (London, Paris, Amsterdam, Frankfurt, etc.) and involve transferring to a USA-flagged carrier's code-share partner. This is normally pretty painless and routine and after 9 or 10 hours on a plane, you may enjoy the chance to walk more than 50 feet at a stretch.
If you want to fly into one of the smaller Italian airports like Florence, Pisa or Bologna (to arrive close to where your daughter is studying), you will definitely need to 'two (or three) hop' the flight.