I guess the overall answer in a campground, whether it be bringing dogs or having campfires or playing that rock & roll music those darn kids like, is be respectful of others. Campgrounds are shared space.
We also notice that when campers with dogs introduce themselves, let the neighbours get to know them and their pets (not while they're three-leggin' it on a tree, but afterward maybe) it does a lot to improve things. Hard to complain about a dog you just petted.
Also, the 'OK to pee on the tree' thing does NOT apply to the owner.