We did a similar trip two years ago (my kids were 10 and 13). My parents lived in Tucson, so we started there. Tucson to Painted Desert/Petrified Forest. Then to Sedona. Then to Bryce and on to Vegas.
I highly recommend Painted Desert/Petrified Forest. It was amazing and otherworldly. Easy walking trails for all ages.
In Sedona we did a Pink Jeep Tour which was fun--especially for the kids.
Grand Canyon is amazing, but some of the smaller canyons (Walnut Creek) are really impressive and a little more accessible.
We did a horseback riding tour down Bryce Canyon that was 100% worth it.
In Vegas we stayed at NYNY, which the kids thought was superfun AND it was budget-friendly. We did the Blue Man Group show and also took a trip out to the Hoover Dam. We also picked a couple of buffets on the strip--the kids loved the fancy choices and being able to eat whatever they wanted. So much to see in Vegas--and we're not gamblers!
Be sure to do the Jr Ranger Programs at the National Park sites. They're really good and will help your kids stay engaged and appreciate what they're seeing. They also get cool badges, which my kids enjoyed.
Jen
"What we permit we promote."