We did a similiar trip when our sons were 12 and 14...and loved it. We flew into phoenix and flew home from Vegas. (If your kids are baseball officianados like my boys you can tour Bank One Ballpark when you get off the plane and then be on your way)
We did not go to Hoover Dam as the "mini" tour is only available since 9/11 and we were told numerous times that it was not worth it. Definitely leave Vegas for the end as it is more luxurious- you'll see what I mean if you do.
Here's my advise:
Stay in the parks - Bryce Canyon Lodge and Zion Lodge are right there...not expensive and if you cannot get reservations now you will be able to get the week before as people cancel.
Do not spend more than overnight at the Grand Canyon...it's nice but Bryce and Zion are more manageable with kids your kids ages (ie hiking, horseback riding)I would suggest the mule/horseback riding in Bryce and the hiking in Zion. I would definitely agree with the other person who suggested the horseback ride on the Indian reservation.
If you go to Sedona please take the kids on the Pink Jeep tours - awsome!! - and stop at Slide Rock state park on the way to the Grand Canyon. There is a natural water slide there.
In Lake Powell stay at the Wahweap Lodge - Either be prepared to rent a boat and take the kids on floats behind the boat or only stay overnight for one night as it is beautiful but boring. You can take the 'Smooth River Float Ride" when you stay there but you have to get it at the dam in Page, AZ.
I can only tell you that it was a trip of a lifetime.