17 Days in Italy!

Have you considered what is called an "open jaw" flight? That means arriving in one city, departing in another. In this case, fly to Venice, then train to Florence, then Rome. Or reverse order, depending on airfares, etc. That being said, here are other thoughts:
Day trips out of Florence will be easier by leaving out of Florence to Lucca, Siena, Pisa, Bologna, CT. No need for a car. Consider more than a day trip to Siena. I can no longer recommend CT due to overcrowding. Give yourself more than two nights in Venice. Consider making a long journey via train from Venice to Florence by way of Verona, then to Bologna and arrive later in the day at Florence. Regardless, rethink the trip so you are not backtracking and spending so much time criss-crossing the country.

You're making some smart choices: you're not driving or doing museums on your (jetlagged, exhausted) arrival day. Instead, you'll make good use of what's left of that day by pressing on to your actual destination. You're putting your days in Rome at the end of your trip (because you have to spend your last night there anyway since you fly out from there). You're not doing a string of one-night stands. All good. Overall, not a bad pace, but a couple of items I'd suggest...

You're counting the same day twice in many cases: April 21 is listed as part of "Florence to Venice", then it's also listed as part of "Venice to Tuscany." You list other days the same way (that is, you may be "crediting" that day to two different places). That doesn't seem realistic, in fact, because it looks like those are days you will travel from one place to another, you should probably not "count" it as a usable day in either (the day is mostly consumed just by relocation and travel logistics). Fortunately you are not slicing your days way too thin (a common mistake) so this is mostly just a suggestion to be careful in how you allocate your time (just remember that internal travel days will eat up most of those days, leaving you with little usable time on those days).

Remember that "X nights" anyplace gives you X-1 days actually there. So your 2 nights in venice gives you just one day there. Venice is unique and IMHO worth more than one day - even in a fast-paced trip, I'd give it a minimum of 2 full days, maybe 3 (and I was cynical about Venice before going there; it charmed me).

Most folks advise against doing CT as a day trip. Because everyone does it as a day trip, and you see it at its worst - terribly crowded. Better to arrive mid-afternoon, spend the night there (when the crowds clear out), enjoy the evening and next morning, then get outta Dodge by late morning when the crowds swell.

Can't help you with your question about public transport on Labor Day; I'd imagine that some things would close that day but basic public transport to the airport would be business as usual.

Good luck and congrats on the nuptials.

If you can't do multi city flight (either because already booked in and out of Rome or ridiculously expensive), I would go to Venice on your arrival day. It is the furthest place you are traveling to. I would move 2 days from Florence/Tuscany portion so you have 4 nights there. Realize you will be jet lagged the first day so this will give you three days.

Then go to Florence. Rent a car in Florence at the end of your stay and do your Tuscany agriturismo. But note that some of the places you say you want to travel to are actually easier from Florence (Sienna is an easy bus ride and Lucca and easy train ride). So maybe reconsider your allocation of time between Florence and San Gimigano here.

Then go to Rome as you have planned.

Congratulations! I hope you have a wonderful trip.

.Day Trip to CT???

Do more research. Day trip to CT is almost as nebulous as saying "day trip to Florida's panhandle" or "day trip to the New England coast". Furthermore, a day trip puts you in the region at the worst possible time. That's when the cruise ships disgorge their passengers and, well, the day trippers arrive. CT is best early morning or early to mid evening.

Rent Car at: ???

I'm thinking Siena would be your best bet. You can train from Venice to Siena. It's a fairly short drive to San Gimignano. Have you found an agriturismo yet?

Here's a quick rundown on driving. Get your IDP from AAA. Google "driving in Italy" and study up on the signage. Learn what a ZTL sign looks like (it's easy). Strictly obey speed limits and ZTLs. Assume any area within the walls of a hill town is ZTL. Park outside the walls. There's usually plenty of parking. We spent 10 great days driving all around Tuscany and didn't have any problems or surprises.

Possible Day Trips: Bologna, Lucca, Sienna

Personally, I'd concentrate in the area around San Gimignano. Bologna would be 2 hours away and unless you have a compelling reason to go, I'd wait for the next trip.

You won't have nearly as much time as you think. I suggest you leave one day in Tuscany as a "free" day, probably the last day you are there. You'll hear about interesting things once you get there and if you leave open a down day, you can go exploring the unexpected.

Again, here's best wishes for a long and happy marriage. My wife and I shared our first kiss in Florence on a school trip when she was 14. This August we'll celebrate our 50th wedding anniversary.

Consider Open Jaw.
Trips to Lucca, Pisa and Sienna would be nice. Bologna is OK, but we preferred Ravenna far more.