We are planning on visiting October 3-10. 3 nights in Las Vegas onto to the Grand Canyon for a short hike on the South Rim with one overnight and onto Tucson/Dove Mountain for 3 nights.
Is it worth it to drive to the Painted Desert en route to Tucson? I've been told it's too beautiful to miss.
Also, any recommendations for the overnight after hiking the Grand Canyon?

You can exit the Grand Canyon via the East entrance and get a view of the Painted Desert.

I would overnight inside the park and leave in the morning.

I recommend you stay right at the south rim in any of the hotels there. They are all run by concessionaire xanterra.com.

There are 4 literally right on the rim (El Tovar/Bright Angel/Thunderbird & Kachina, and two only a short walk away (Maswik, Yavapai). A room in any of them will be good for one night.

Thank you for your replies. We are going to make a request for Phathom Ranch and if we get it we will stay over in the canyon. If we don't we will stay on the rim and leave via the east entrance.

Phantom ranch does not classify as a short hike... Depending on your fitness level it takes half a day to get there, and up to a full day to get back up to the rim. Many miles of trail and a 5000' elevation gain.

Phantom Ranch hike is great but really strenuous if you are not an avid hiker. After the Canyon drive off the highway south of Flagstaff and go through Oak Creek Canyon and Sedona instead. In fact, make that area your destination instead of the Painted Desert and come back for a southern trip. There's so much to see near Tuscon, it is it's own trip. Also, when just north of Phoenix, get off highway at Rock Springs and go directly to Rock Springs cafe for chicken fried steak, coffee, and pie, and soak up the atmosphere. It's right off the exit. Have a blast!

Phantom Ranch was probably SOLD OUT on 1st October 2013 for October 2014. And as the others have said, it is not a "short hike". Approximately 8 miles down the South Kaibab Trail and approximately 10 miles back up the Bright Angel Trail, with an elevation loss and gain of around 5,000ft.

I' too, would save Tucson for another visit and instead spend some time in Sedona. Tucson is 5 1/2 hours south of the Grand Canyon.

If you exit the GCNP by the east gate, you can still see quite a bit of the painted desert. If you lave the GCNP early enough, you could still do the detour to drive through the Painted Desert / Petrified Forest NP and still drive through Oak Creek Canyon to get to Sedona before sunset.