Normally I would say Tetons to reduce your mileage. But for you it only adds about 300 miles.
Then I saw your plan and will definitely say you don't have enough time in Yellowstone.
I would suggest:
2 nights out
3 nights drive through Jackson and Tetons
4 nights Yellowstone
2 night Bozeman (visiting an old friend)
1 nights back
Or possibly even drop one of the Teton nights for another in Yellowstone.
Edit: On review, you are a few days short if you have two weeks. Two weeks is good for 15 nights assuming you leave on Saturday and return on the 3rd Sunday. Your trip schedule is only 12 days so you still have 3 to add.