It pains me to spend this much time in a car in a foreign country but
we want to see everything.
You won't get to see everything. You'll spend your vacation days seeing lots of asphalt and boring highway scenery. There's no way of seeing all of Greece in nine days (notice I am not counting your arrival and departure days).
Of your total of eleven days of vacation, you've basically got four real sightseeing days only and seven travel days. To each his own, but for me, that would be a terrible ratio.
I don't agree with the opinion on Santorini expressed above (to each his own here too, of course); on the contrary, I think that Santorini is a great place to see especially for first-time Greece visitors. Yes, it is crowded and touristy and not "authentic", whatever that may be, but it's beautiful and spectacular nonetheless.
What doesn't make a lot of sense to me is spending basically three days of my valuable vacation time and getting only one full day of Santorini out of that. In your case I would have said: Stay on the mainland, that's more than enough for your nine days. But since you have already booked Santorini, I guess it's too late for that.
With those plans already fixed, I guess it's also too late for recommending that you put the Athens day at the end of your trip, which would give you more safety for your return flight. I agree with the others that I wouldn't want a long drive on the day that I have to catch my return flight. You may get caught up in bad traffic, or just imagine having any issues with the car... and you can wave good bye to your plane.
Also, you'll be pretty jetlagged on that first day and may not feel up to doing much sightseeing anyway, so it would have been a perfect day to move right on to Santorini and relax with a caldera view. Any chance of moving those Santorini dates still?
You haven't told us what time of year you will be going. Might be helpful to know for more advice.