Coley,
This is a tough one, because both areas are very different and very beautiful!
My daughter and I visited Chamonix, Annecy and also a few places in Provence (Avignon, L'Isle sur la Sorgue, St. Remy and Les Baux) last June. We enjoyed both areas and certainly wished we'd had more time in each of our destinations.
As Laura has pointed out, it's ideal to have a car if you want to visit many of the small towns & villages in Provence, however you can visit some via public transportation (train/bus). We didn't have a car so we didn't get to Roussillon or Gordes.
Having said all this, Annecy became our favorite place!
It's a very charming town with a crystal clear lake, good food, and beautiful atmosphere.
We also enjoyed the street (farmer's) markets in Annecy (and Provence.
Here are a few websites to help you decide where you want to spend your time:
You'll have a great time wherever you choose to go because you'll be making lasting memories with your daughter!
Enjoy!
Edit to add...
I took so long to write my response (distracted by my dog barking at the gardeners, etc..) that I didn't realize that you had added a response. If you choose to go to Annecy and Chamonix, you don't reallly need a car, however, if you choose to go to Provence, then a car will be great.