There is plenty to do in Tuscany, so trying to tack 2-3 days on the end for Venice or Amalfi Coast doesn’t make for a relaxing or rewarding leg. They deserve more, but on a return trip. If you absolutely wanted a 3rd location, then Lucca or Siena jump out, but personally I’d try to stick to 2 locations. You’re keen to do the tourist sites, see the architecture, but also taste some wines. The plan seems to be shaping up nicely against Florence/Firenze and a rural location in wine country.
Your thoughts of 3-4 days in the city feels about right, and I’d lean towards that as the start. Whilst the countryside gets you over jetlag quicker IME (natural light at the right times, over artificial light into the evening and night), getting out and walking also works well. In addition, it can be stressful having to adjust to driving in a foreign country straight off the plane. Just a few days on foot allows you to get adjusted & familiarise yourself with basic road signs etc. Finally, if you get carried away with wine shopping, it’s easier to lug from the car drop-off at the airport than from the city.
This also means that 6-7 nights can mean you don’t have to ignore weekly apartment rentals in the countryside (still quite common to have set weekly slots).
Patrick’s advice re: booking in advance for the Uffizi is guidance that I’ve seen many times on Slowtrav forum who are generally a clued up bunch. I’d follow his advice if you want to go there.
As for rural Tuscany, the driving is generally pretty easy & relaxing, but will get more stressful in the towns - and for the more famous ones, do work out in advance where the ZTL zones are to avoid a painful fine. We tend to plan in advance, either looking up online or asking in the agriturismi we typically stay in, where a good place is to park. I’ve no problem parking a few 100 yards further out to avoid stress.
As wine is clearly an interest, what about trying to stay in one location that allows you (at least on one day) to leave the car parked up, and stroll to the wineries (ideally ones you really would like to make it to). Italians seem horrified we might walk half a mile to get to their winery, but you’re in the countryside, often in lovely weather and on holiday, so I don’t see the problem, even if you have to occasionally hop onto the verge whilst traffic goes past. Even if buying a bit of wine, you can always arrange to pop back another day to pick up the wine in the car.
Finally wrt wineries, try to slot the odd lesser known or even unknown winery, that seems to be making a modicum of effort towards quality. We’ve discovered some lovely gems this way (Daviddi in Montepulciano jump out in Tuscany form our travels). They may be a fraction off the best, but not as far as you’d assume, and the prices are often very good. Add to this that you’ll be bringing back something that isn’t in the shops at home, and that often comes along with the warmer and more hospitable welcomes. Indeed one well-known & well-regarded Tuscan winery gave us a hard sell at the end of a winery tour we’d paid for (most don’t charge in our experience), the only time anyone has ever attempted to pressurise us to buy in Italy (nor indeed any winery in Australia or New Zealand either). I was quite dumbfounded to encounter this. Daviddi in comparison brought us fresh towels to dry off with after getting caught in the rain, and dropped us off in the car at our next winery visit! That typifies the amazing hospitality you can find in Italy when venturing a little away from the famous / obvious.