Just random thoughts from our experiences as high-energy breed owners:
A "walk" on leash sometimes is more tiring than allowing them to rip and tear offleash; plus it helps socialize your dog to the campground lifestyle (noise/confusion/distractions)
If you ask at the front desk - many folks will tell you where you CAN run a dog offleash. Sometimes it's a back lot of the RV Park; or a property adjacent to it... BUT... (and this is the biggest "but" of them all) - your dog had better have a "Bombproof recall". As in "My dog will break off a squirrel chase to return to me". Having your pup run off to challenge a pack of coyotes, (or a skunk) for example, is a really bad thing.
No offense - but you're going to have a huge rambunctious puppy and little kids all cooped in a small space if you full-time. Right now I have a 12#, 6-month old pup and NO children and I can't imagine full-timing in an RV....LOL!!! But you might want to really look hard at how much frustration your plan can cause for everyone....