The Garner "cabins" are actually screen shelters (roof, concrete floor, windows, but no A/C or restroom built-in) and they go quickly in the summer which is Garner's busy season. Camping in a tent's just fine out there -- indeed, it's what the majority of folks do. That, or you could rent a pop-up or other trailer and live in veritable luxury.

We rented a pop-up camper a couple years ago for a week-long camping trip in Big Bend National Park and it was quite enjoyable for the two of us. Plenty of room for a couple kids, if we'd rented a slightly larger pop-up or hard-body camper. It might be worth considering!
Other parks that families find very enjoyable, due to the number and variety of amenities/recreation opportunities, include:
Choke Canyon State Park -- boating, fishing, swimming pool, basketball court, screened shelters,etc),
Bastrop State Park -- small but beautiful park in the "Lost Pines" of Texas; swimming pool, 12 cabins, a pond for fishing & pedal boating,
Guadalupe River State Park -- tubing down the Guadalupe, fishing, hiking, lots of campsites but no cabins. There are others but these are the first off the top of my head. Oh yes, on par with Garner (and just as busy, so get reservations ASAP) is
Inks Lake State Park -- pink granite like Enchanted Rock but with a lake as the focal point; hiking, swimming, etc.
Have a terrific summer!