Driving between Parma, Carrara and San Minato

Italian drivers are generally good drivers, and less personally aggressive than, say, Boston drivers - way less. However, as everywhere, some behaviors are seen as unacceptable. One trigger is not keeping to the right except to pass on a multi-lane road. The rule is exaggerated in Italy by some drivers to add - 'and not inhibit me from passing even if I'm going insanely fast'. This is enforced by extreme tailgating and the flashing of brights (now illegal, but still seen occasionally). If a US driver learns European signage well, is accustomed to city driving, and has the right temperament, driving in Italy is not difficult.

Well only you two can work through that previous issue, but I would drive at least part of the trip. You can easily take the train from Parma to Carrarra (see the Trenitalia website), but you need to work out where you are staying first. It is not a day trip distance, so we need more information about your plans.
Again, you can get to San Miniato, but you will likely want a car for the surrounding area. I am heading there for the first time next month, and as I understand it, the train station is not close to the old town, so you would need to take a bus or taxi once there. I am unclear if you intend to stay there, etc.

Actually Carrara train station is a long way from Carrara the city and the quarries are quite a ways from the city and spread out. The old part of Carrara is uniquely interesting and the Duomo is excellent with Michelangelo's workshop building just behind it. I recommend a tour to see the quarries although you'll get numerous impressive views of the quarries and mountains if you drive up to the village of Colonnata (with or without tasting the lard).
Search 'carrara tour' in the box above to see a recent question on tours with links.

Not all drivers are aggressive and crazy in Italy, some are aggressive and crazy in the US as well (including me, at least according to my wife), certainly here in the SF Bay Area. Generally drivers are more aggressive and inpatient in places that are marred by congested traffic, therefore, people in big cities, like SF, NYC, Boston, Rome, Milan, etc. will be generally more aggressive than people in more rural areas. It's probably because of the frustration that builds up in people when they constantly have to deal with bad traffic.

I don't know where you plan to rent a car and go exactly, but Parma to Carrara, and also Carrara to San Miniato is almost entirely on freeways. Driving on Italian freeways may be stressful for many Americans, because Americans often cruise in the left lane, and that is a definite no no in Europe. The left lanes should be used exclusively for passing and reentering immediately to the right lane after the passing is complete. If you linger in the left lane while a faster car wants to pass you, they will flash you and tail gate you inches from your rear bumper until you move away, and that can be unnerving. So use the left lane with extreme caution, move the left only when nobody is coming at full speed, then move back to the right as soon as possible. While passing on a freeway also be aware of big trucks. They are big and they don't care, they move to the left lane without signaling sometime, so be careful.

Driving outside of cities on regular two lane roads is not difficult or stressful. Many roads in Tuscany are curvy since the terrain is mountainous. If you plan to drive to the marble quarries on the Apuan Alps, above Carrara, roads are very narrow and curvy with deep ravines.

Grazie mille, fellow travelers. I hope your journeys are soul-satisfying!