Some people are very cautious about driving at all on arrival day. I'm not, but also I know myself and I'm always fine on the day I show up to Europe.
But I will say, if it was me I would be taking that car straight to the place where I was going to sleep. You might be dead tired and lightly disoriented. Probably you'll be fine, but personally I don't do more driving than "necessary" on transatlantic arrival day.
But outside of that:
For one, I bet your agriturismo is awesome, and will be a wonderful place to spend a first late afternoon and evening. The trip to the hot springs is not opportunity cost free.
And second, I don't like the way it feels when I am extending my transit time coming from the United States. I don't like adding interim stops that aren't the place I'll sleep. I prefer feeling that the travel is done and dusted, and I am at the place where my trip is starting. So if I went to the hot springs, I would likely be mostly thinking about getting back on the road, not able to fully relax and enjoy.
And all of that is just me of course, like any other opinion, take it for what it's worth. Have a wonderful trip to fabulous Italy!