We spent 4 months workamping in Alpine Texas which is about 100 miles from the Headquarters of Big Bend.
The headquarters is about 25 miles inside of the park from both entry points of the park.
After going to the park 4 times and telling many folks about it here's what I can report and recommend.
As many said you can not get your rig into any other campground INSIDE the park except the Rio Grand Campground. This campground is at the far east part of the park and is fairly remote to everything else in the park. It does have hookups and a small store there that has sandwiches and supplies. As said by some one it is all concrete parking but does have grass and picnic tables nearby. This is also the only place that takes reservations in the park.
The resort at Lajitas is great if you like to play golf but I am not sure what they would have for kids to do.
The Stillwell Ranch is 8 miles outside of the Persimmon Gap entrance. It is rustic and has little shade. Full hookups and great wifi though. The museum is great as well. But there will be little for the kids to do except ride bikes if you bring them.
Terlingua has a couple of RV parks and, unfortunately, I do not know much about them. We did hear a few good remarks about the Big Bend Resort and Adventures and they are located very close to the Highway 118 entrance to the park.
Outside of the immediate park area there are several small towns. The largest one of these is Alpine and this is where we workamped for the winter last year.
Now, I am not only recommending the park we worked at because we worked there but because we made it a point to visit all of the RV parks in Alpine, Marfa, Marathon and Ft. Davis.
Other than Ft. Davis State Park the Lost Alaskan is the nicest park you will find in the entire Big Bend area.
It does have a nice play ground and pool and splash pad (however not sure it will be open in October) and the cleanest shower/bathrooms and laundry you will ever find in an RV park. There is also a small fenced area for the dogs to be loose in. The owners live onsite and take very good care of the park.
One thing I am sure you are aware of is most places rates are for 2 or 3 people and there is an extra per person charge for the rest in the party. At Lost Alaskan it was $3.00 for any more than 2 people and everyone else over the age of 3. This is due to the extra use of water for showers and the extra strain on the sewer systems.
Alpine is a nice little town with several great restaurants and shops. If you go there be sure to eat at La Casita. It is the best Mexican food in town. They also have several fast food restaurants and a Pizza Hut.
If you have time try to drive up to Ft. Davis. The fort is a great place to visit and so is the state park there. A great place to eat here is Maddog's Cantina...the best Philly cheesesteaks and French dips in Texas!
The McDonald Observatory is a great place to visit with kids as well.
While you are in the park be sure to drive up to Chisos Basin - it a beautiful drive and the rock formations are outstanding.
Also be sure to drive down to Santa Elena Canyon. It is another beautiful drive and when you arrive there you are at the base of a 1500 foot deep canyon that has been made but he Rio Grande River.
The best thing to do is have a great time in this beautiful part of Texas.
Oh - and one other thing - the closest Walmart store is in Ft. Stockton TX. Alpine has 2 small grocery stores though but if you can stock up in Ft. Stockton.