Another option is to visit Big Bend Ranch State Park. It is every bit as rugged and beautiful and maybe less developed than the National Park. There are no sites in the state park appropriate for a trailer, but there are private RV parks in Terlingua and Lajitas. We've stated several times at Maverick Ranch in Lajitas. It is full hookup, and sort of in the state park, and sort of $$$.
Keep in mind that most of the non-desert hiking in the national park is in the Basin. The road to the Basin has a 24 foot vehicle length limit; believe this limit. The two lane road has no shoulders, steep grades, and hairpin or worse turns.
Get reservations if you can; the parks can be crowded around Christmas.