Sound like a great trip planned. The southwest is such a fun place to explore. Here are some other possibilities:
: small but fun historical way-point nestled in a box canyon. Have had the small campground all to ourselves a couple times.
: arches and lava tubes to explore, although looks like the lava tubes might be closed due to bat fungus? Some fun mountain biking too.
Chaco: awesome place. Spent a week there doing every possible hike on the NPS map.
: I 2nd this recommendation, although it looks like the main attraction, Alcove House, is closed. Lots of hiking though.
: very small park but a reconstructed Great Kiva that is impressive.
Canyon De Chelly
: "living" park, as in some of the generations of native americans that have lived there still live there, farming the land, or giving tours to the rest of us. Awesome, magical, alive place, but can also be a little sketchy.
: worth the trip just to read the letters that the rangers compile from people returning "borrowed" pieces of petrified wood.
: both on the same loop road. Hike through a lava field and and cones from an eruption 900 years ago then check out ancient pueblos.
: cliff dwellings but on a much more intimate level than other places I've experienced. I think this is my favorite of all the places like this because the canyon is so unique, and they allow you to walk through some of the dwellings, that it is easy to get a sense of what life might have been like.
: a bit touristy but instantly recognizable landscapes from cartoons to movies.
: small park but the 3 bridges are great. The bridge loop hike may be a little long for kids at 8.6 miles, but one of the top 10 hikes I've done. There are "hidden" ancient dwellings and other things to find back there that the NPS doesn't put on a map do have ammo-can-stored info and sign-ins when you find them. Nice campground too.
: like a mini-Bryce but at 10,000 ft. Should be open by the time you're traveling. This is the park that William Least-Heat-Moon was trying to get to when he got to the closed road and had to wait out the snow storm in the van. Nice campground too.
: unexpectedly nice canyon right outside St George with lots of family friendly hiking opportunities. Spent a couple days here a few weeks ago. Nice campground, with showers too.
Hope this helps.