We were campground hosts at the Chisos Basin Campground about two years ago Apr-Aug.
The road into the Chisos Basin is 'restricted' to trailers under 20 feet, RVs under 24 feet. We had no problem taking our 36' foot trailer in, nor another host with a 40' motorhome. However the two hosts sites in the campground are the only ones that could hold your rig. Also, once past the first loop, you would not be able to turn around in the CG. Your rig can't make the turn at the bottom loop, nor turn in the middle loop.
(When I say bottom loop, the campground elevation changes about 150 feet from the first/ upper loop near the entrance to the turn at campsite 60 on the bottom end of the CG.)
Full hookups - as mentioned the parking lot at Rio Grande Village is the only option within the park.
Big Bend is BIG. It takes a long time to get from one place to another. Hour drive between Rio Grande Village and the Chisos Mountains. Another hour to Santa Elena Canyon.
If your stay outside the park, you are looking at a minimum of one and one half hour drive to the 'attractions' of Big Bend from your campground.
Maverick Ranch listed above is probably the best in the area. It is 20 miles of 70/60 mph road to the park entrance. Another 40 miles down the Ross Maxwell Scenic Drive to Santa Elena Canyon.
30 miles from the park entrance to the Chisos Basin, 40 miles to Rio Grande Village.
There are a few full-service campgrounds in Terlingua / Study Butte near the west entrance of the park. Maverick is the only one that has a pool.
There is no swimming allowed in the Rio Grande River within the park.
Big Bend is a unique, special place. Temps will be hot anywhere you can park your rig, but enjoy the park.
I highly recommend taking a day to drive the Ross Maxwell Scenic Drive. There are several stops with short hikes to enjoy to various historic sites. We like hiking down the bottom of Tuff Canyon. And Santa Elena Canyon is a wonderful/ must see hike.
There is one very small store in Lajitas, and another with a bit better selection (Cottonwoods) near the park entrance. Be sure you are stocked with food before you get south of I-10 if coming from Fort Stockton, or Alpine if coming in from that direction.
Bring plenty of water. We saw many hikers dehydrated during our stay. Humidity levels are extremely low at Big Bend. The sweat evaporates off your skin before you know you are sweating. People often underestimate the amount of water they need.