Perhaps a Modification or Two
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You actually have the makings of a very good week plus RoadTrip through some of the great natural wonders of the American Southwest. I would, however, suggest just a couple of modifications. I would skip Grand Staircase Escalante National Monument and the Page area, both because they are a bit off from and slightly complicate what is otherwise a nice round circular trip, and because there are at least as good or better options. I would do the trip in a clockwise direction, because we drive on the right (as opposed to left) side of the road making right turns is easier and because doing so means that when you drive through Grand Canyon National Park, the canyon itself (and parking lots) will be on your side of the road.
Instead of Grand Staircase and Page, I'd add Arches National Park and Dead Horse Point State Park. Your basic route would then be from Las Vegas up I-15 into Utah and take UT-9 east to Zion. Then continue east on UT-9 to US-89 north. UT-12 will take you to Bryce Canyon, but return back to US-89 and continue north to I-70 east. This is itself a great scenic road which you'd take all the way to US-191 south which will take you to three destinations. First up is UT-313 into the Island in the Sky District of Canyonlands National Park as well as Dead Horse Point State Park. Returning to US-191 south next up is Arches National Park and finally, via UT-211, the Needles District of Canyonlands. Note that the various districts of Canyonlands are not internally connected. After Canyonlands continue down US-191t US-161 to Monument Valley. this is a Navajo Nation Tribal Park, not a national park, so your national parks pass ($80 at the first park you come to) will not work here. I would also heartily recommend that you hire a native guide and his high clearance four wheel drive vehicle rather than try to drive yourselves over the very rough roads. Continue south on US-161/US-160/US-89 to Cameron, with a stop to window shop at the Cameron Trading Post, to AZ-64 through Grand Canyon National Park. AZ-64 will eventually bring you out at Williams and then it's just a short hop on I-40/US-93 back to Las Vegas via Hoover Dam.
A couple of other things worth noting. As mentioned above, the annual parks pass is probably a good idea if you are going to be seeing four or more national parks and monuments. It covers entry fees (only) to all parks in the system for everyone traveling with you. There are also a number of other smaller parks and attractions that you'll be near on your circuit that you might want to check out especially in the Flagstaff area including Wupatki, Sunset Crater and Walnut Canyon National Monuments, Lowell Observatory, and the Museum of Northern Arizona. And at every park you come to, check in at the visitors center or ranger station. They are a font of knowledge about their respective parks and can certainly direct you to shorter flatter hikes that will allow you to get the most out of your visits even with reduced mobility.
AZBuck