We've done all that, it's all good and very difficult to say what would be better. Other factors may help with the decision, like,
rv or tent, can you drive long distances with out "are we there yet" going on the the back seat, and the price of gas.
Palo Duro was amazingly beautiful, but it was warm in June last summer. We did several day trips to see things in the area during the day and enjoyed the park in the evenings. There is no swimming there so we did drive to the community pool in Amarillo, if you go, go early as the local teens overtake the pool by 3. We stayed in the Mesquite campground and it was very canyonesque compared to the hill country like Hackberry area. Sagebrush is their newest loop, at the highest elevation, added when juniper was forever destroyed by flooding. There is a stable in the park for riding.
Caprock Canyons was a jewel. Out in the middle of no where, no DQ, no stop light, just a blinking yellow where you turn to the park, it was solitude +++++. The water electric sites are on the prairie level, so wind was a factor, some sites had a tree, we had #13, and the tables are covered. The bunnies filled the field around the bathhouse in the morning. If you can, camp in the water only area of South Prong. Once you drive past the shower house, the road drops off into nevernever land. I would stay down there and drive up to shower a night ( if we ever get back that way). The lake was a great place to swim and stay cool. We spend hours there. I am picky about lake swimming and really liked it. There is a local guy, Mr. Tomas, who came out with horses for us to ride with him. The ranger gave us his number. Their VC has a great buffalo exhibit as they are home to 65 of the state's buffalos. Palo Duro has just a few. There is a drive in theatre between Quitaque and Turkey, we saw the Indiana Jones Movie. Bring what you need, if you don't, make sure you check the expiration dates on items from the convenience store.
Balmorhea is a great place to swim, or use as a base camp for you day trip ( 2 hour drive ) to Carlsbad. Carlsbad was cheap and worth the trip. Unless you have a trailer, I would not recommend camping at Balmorhea, it's 10 degrees hotter than Davis and the showers are on a timer.
Davis was nice. We had #44 at the end of the cul-de-sac. Saw grey foxes and a mule deer doe. We had the entire loop to ourselves the entire trip. The observatory was nice, although the kids got bored quick. The fort kept their interest much longer. Nice places to eat in town. We also drove to Alpine to the Woodward Rock Ranch and dug up red plume agates, this was fun and something different. The owners were super sweet and a bit excentric.
The ghost town of Terlingua is just outside Bid Bend. It was interesting, but unless you are going to see big bend, save it for another trip. Big bend deserves at least 7 days of your time to fully expereince it.
I would do separate trips. In June, do west Texas. Although it is desert, at the higher elevations it was pleasant.
Leaving on Saturday,
Drive to Junction and camp there 1 night (swim upon arrival near park entrance)
drive to Balmorhea and camp 2 nights (drive to Carlsbad the first day and swim the next, leave for Davis late afternoon, 30 minute drive)
drive to Davis and camp 3 nights (visit the fort, the observatory, hike, get ice cream across from the fort from the caboose, and avoid the restaraunt at Indian Lodge, eat in town, drive to alpine to dig rocks, go back to swim at balmorhea if the kids are frying)
drive to Junction and camp 2 nights (swim in Day use area #2)
arrive home Sunday with sunburns and smiles.
Search the site here for our previous trips for EVEN MORE details.