Thank you for your advice!
Our program is now the following:
day1 : SF
day2: SF - Crane Flat (yosemite)
day3: Crane flat
day4: crane Flat - Lone Pine ?
day 5: Lone Pine? - Lake Havasu?
day 6: Lake Havasu? Grand canyon
day 7: Grand Canyon
day8: Grand canyon - Monument Valley?
day9: Monument Valley? - Lake Powell?
day 10: Lake Powell?
Day 11: Lake Powell? - Bryce?
day 12:Bryce? - Las Vegas
The items with ? are not booked yet. Any suggestions are welcome! I also find it difficult to find the right campground. Do you have suggestions for that as well?