I've been from NC to Texas (18 hours each way) with my wife, daughter, and in laws twice. First time, we barely survived, second time was almost enjoyable. Smart to take only immediate family. I think for all the reasons mentioned above your better off renting a smaller vehicle and getting a room.
I'm taking the wife, daughter, and a friend of hers to Pigeon Forge/Gatlinburg in a couple of weeks. I love to tent camp. We need a new tent (@150-$200). Tent sites with water and electric were @$40. I found a small cabin with a double bed, bunk beds, cable TV, AC, toilet and sink for @$50 a night. Guess which one I choose

I'm going to the knife show, the campground has a nice big pool and good clean shower facilities.
We plan to take our pop up shelter and a big cooler and drive the wife's crossover that gets @19 mpg on the highway (its AWD) and she's got a heavy foot. I think it's a great compromise that makes everyone happy, including our check book. With what we save on lodging, food, and entertainment, we can possibly let the girls do something really special, something they'll never forget.
Oh, and if your family balks at the idea, rent that RV movie with Robin Williams
GregB