From Monticello to Page, it's also nice to stop by the Natural Bridge NM. I'd suggest to arrive Monument Valley NM in late afternoon. It looks a lot better near sunset.
If you are going w/ kids, prepare 2 hrs more time at each NP for them to participate the Junior Ranger programs which they seem to enjoy better than the parks itself.
Also, store enough nice snacks & water in the car. It's not easy to find a nice place to eat on the road or in the park. You can shop at Moab or Page. The gas price was actually cheaper at those two locations in late June.