Houston to Destin should be less than a day's driving, particularly summer.
On a trip in late February, with shorter daylight hours, leaving San Antonio 9 AM put me in Slidell at sundown. From Houston, the Pensacola - Panama City area, your destination, would be my likely overnight stop.
There are a number of decent RV parks close to I-10 in the Gulfport-Biloxi area. That would be beyond the halfway point, about 6 hours out of Houston. Halfway point is somewhere between Baton Rouge and Slidell if destination is Panama City.
I can't select a Biloxi area RV park for you, I prefer the more primitive CG at the National Seashore.