Driving to Praiano from Siena

First something on Siena.
Siena's historical center is closed to non resident traffic, therefore if you stay in Siena proper for that week you need to be mindful of that and try to find a place outside of the city walls. Better yet, would be to stay outside of the city altogether in a smaller town or in a farmhouse. You can visit Siena from there, just park at any of the parking lots outside the city walls (near the stadium there are plenty and it's a short walk to the city center).
On Siena-Praiano.
You definitely should drive. Trains and buses are possible, but since you already have a car it makes no sense of going through the hassle of taking 3 trains and one bus. Much more convenient to drive, especially if you have luggage. The drive from Siena is very easy. All freeway from Siena to Castellammare. Then from Castellammare a highway. As you get closer to the Amalfi Coast the road becomes curvy and narrow, but just be careful and you'll make it easily. Don't get scared. Driving in the area is possible the challenges are the expensive parking lots (€25 day) and the congestion on the Amalfi Coast during summer and particularly on weekends. I don't know when you are going, but July and August are congested daily, while the rest of the summer it's more of a weekend thing. Inquire with your hotel in Praiano about parking options. Maybe they have a lot where you can park for less money. Also when you travel around the Amalfi Coast, parking will be the challenge (especially for the wallet).
I don't find the drive on the Amalfi coast difficult at all, but everybody is different and I learned how to drive in Italy. I suggest that you use the Google Street View on Google Maps to try and 'virtually' drive the road from Positano to Praiano. That is the the narrowest and curviest that you will be driving on. You can get a good idea if you can do it by doing that. Personally what people say about it is way overblown. If you know how to drive on a mountain highway in North America, you can drive on the Amalfi Coast. It's just that sometimes people park on the side of the road and make it even narrower than it already is. Parking enforcement is not the Neapolitans' forte.

Terry, instead of driving from Florence to Siena and staying in Siena, you might consider 1) taking the bus from Florence to Siena, 2) staying in an agriturismo very near Siena (we know a few) and, 3) not renting a car until you are ready to tour more of Tuscany. We have done it. You can easily take a taxi to and from the agriturismo into Siena for about 12 Euro each way. No need to find and pay for parking, no need to rent a car and no need to worry about tickets - yet. As for the Amalfi coast, wait until you find out how difficult it is to find parking.

Thank you for the great advice on the driving and parking conditions.

Any personal experience on what are must sees in the Amalfi Coast area and how to best get to and tour Capri on our own? Where to best catch the ferry from Praiano

Amalfi Coast proper is a series of quaint fishing villages perched on cliffs on some spectacular Mediterranean coastline. Positano and Amalfi are the most famous of those towns. They also have nice little coves and small beaches tucked in the cliffs. The Duomo (Cathedral) of Amalfi is nice. All in all it's a great place to sit at a cafe/restaurant and relax while eating seafood and people watching with a spectacular view in the background. There are places where you can hike along the coastline. My favorite activity is spend time at those beaches. If you do the water is deep and it's rocky, so be careful. In a way the Amalfi coast is similar to the Cinque Terre in terms of things to see and do.
I've never stayed in Praiano, only in Positano. But from both Positano and Amalfi they have boat excursions to the island of Capri. Sorrento is not on the Amalfi coast, but is near. Pompeii, is also nearby and so is Naples. You can reach Capri from any of these towns although I'm not sure about Praiano, which is very small.