Hi Sarah, on a different note I noticed that you will only be in Siena for two nights, which means you will only have one full day in Siena.
Siena is expensive so it doesn't make sense to stay there if you are going to spend your time in the countryside. In my opinion, Siena is large enough that it takes too much time to get in/out of town so it's not the best place from which to launch day trips. It's not a small hill town.
I also found driving outside around the perimeter of Siena to be confusing and stressful. Not a deal killer if it's unavoidable, but another reason this itinerary raises red flags for me.
So, I would recommend enjoying Siena for the very short, limited time that you will be there. Then work your itinerary to explore the country side/wineries en route to your next destination. Does that make sense?
PS You have a lot more research to do if you decide to rent a car.