I'll concur with Host Young Gang Mom regarding Disney - there are many strategies to try in doing a Disney trip, ways to save money etc. Disney is not "inexpensive" but there are always ways to save. Indeed it is very, very awesome - dreamy, super fun and non-stop action. Everyone would love it.
That said, before I got far down in the thread to see Disney came up, I had already thought of a Florida Beach destination that you could drive to in one day....the Florida Panhandle, specifically Panama City Beach which is situated on Florida's Emerald Coast, that continually ranks among the top 20 beaches in America. 27 miles of white sand beaches and the gorgeous Gulf of Mexico. The only time not to go there would be Spring Break or maybe peak of summer, like now. Since you are flexible, September/October might be great since the weather will still be great and it will be much less crowded.
There are many fun things to do there such as the Gulf World Marine Park with many shows/exhibits including dolphins, sharks, penguins, sea lions and river otters. Throughout the year, the shows vary but it is recommended to be sure and see the dolphin, reptile and sea lion shows. It's a day full of fun.
Shipwreck Island Water Park ranges from exhilerating Raging Rapids to the calmer Lazy River; there is also a section for younger children and overall a very fun water filled day.
There are hiking trails alongside Lake Powell, within Camp Helen State Park. Both freshwater and saltwater fishing are also available within the park. Swim off a secluded stretch of sand and some awesome bird watching for shorebirds and bald eagles!
At the Coconut Creek Family Fun Park, there are two tropical themed 18 hole mini golf courses (no windmills, I suppose
)) and there also a Gran Maze which is a maze that you can walk through which is the size of a football field.
For more wilderness activities, check out St Andrew's State Park with an abundance of outdoor options and the ability to take a tour boat to Shell Island to sight-see, snorkel, watch for dolphins and jet ski.
In addition, there are air boat rides, pontoon boat rides and so much more. Also, with an abundance of vacation rentals available (the more popular option in Panama City Beach) it is certain you can find something to suit your family size. Oops, I forgot Zoo World, and the National Museum of Aviation - you might not think that to be a fun stop, but given that nearby Pensacola Naval Air Station is a huge Navy base, these types of museums can be LOTS of fun.
I found many beautiful and highly recommended vacation rentals to accommodate six at reasonable rates after Labor Day weekend on www.TripAdvisor.com
I'm not sure if, being from a warm part of Texas, you're necessarily looking for warm/beach vacation. Branson is very popular but I hear mixed reviews....it's a great location for mid-westerners to take a vacation.
I recently drove across many states in June/July and saw countless family destinations throughout the country. I was driving to vacation WITH my family
Does your family have any particular interests that might help us offer further suggestions? There are so many possibilities but they have to fit all the interests of your family; let us know what might be especially fun for everyone.