Both GCNP (make sure you are going to GCNP South Rim) and Sedona need more than an overnight if you plan to see anything.
There are a couple of scenic routes from Palm Springs, but not as interesting as you might want. One would take you through the Joshua Tree National Park but getting to Sedona would be much less direct.
The route through Wickenburg, Prescott and Jerome does not need extra days, but does need some caveats. It is very scenic. The 80 miles of Hwy 60 from I-10 is fairly desolate. Unless you are used to driving in very mountainous areas, about 20 miles north of Wickenburg the ascent into the mountains there may be somewhat scary as it is steep, lots of curves, switchbacks and dropoffs. The driver won't see the scenery.
RedRox advice though is best. Drive directly to Sedona. I-10 to Phoenix, Loop 101 around the city on the west, I-17 to Hwy 179 to Sedona. The drive up I-17 is very scenic. Dropping down to Jerome after ascending the moutains north of Prescott is also circuitous, steep, with lots of curves, switchbacks and dropoffs.
You need to book lodging at GCNP as soon as you know your dates. Do that online not through a travel agent.
Edited: 2:03 pm, November 17, 2012