Texas is very limited for public-access lands. And, "south Texas" takes in territory from Cuero to Laredo and points south...
Anyhow, Parks & Wildlife can give you info about public-access lands. Your relatives might know of some private ranches.
Pork chops? Javelina hams are absolutely wonderful when carefully barbecued, but they won't weigh over four or five pounds each.
But real, real tasty.