How much is too much?

Driving will be slow and difficult in many areas espec if you are thinking late fall to early spring.
Unless you have a strong reason for Turin you may want ot rethink. I was there just bef the Olympics and it is not much more than a big congested italian city. I would opt for other areas instead. you could combine train and car it would be alot more relaxing.

If you have a car you can see everything you are hoping to see with that home base. Don't plan on spending more than 3 nights in any location and you'll be fine.

You could make a big loop from Zurich south to Luzern. Then continue south towards Milan stopping at Lake Como before you get there. Veer off the Autostrada before you get to Milan on your way to Torino. Then head to Aix-les-Bains from there.

The roads will be somewhat slow-going because you'll be traveling across the spine of the continent.

I am only assuming that you have time to do this. If you need to get to Aix-les-Bains right away after arriving in Europe then very little of this is possible. Day trips to each of the places you're hoping to visit won't be possible. They're just too far away from Aix-les-Bains.

Sounds like a wonderful trip. My thought is the same as JS: you might want to rethink Turin, given the rest of your itinerary. But it all depends on what you want to do and see. A rental car gives you flexibility, but some travelers are blindsided by the fact that in many of the European countries (say, outside of Germany and Austria) renting a car is not necessarily the cheap, stress-free, and easy option that it is in the US. The pluses and minuses of European car rental has been extensively discussed here and to find those discussions you can use the search box (upper right corner).