the campgrounds that I've stayed at have always had some sort of rough, unused area that I can take the dogs to. Sometimes it has just been a mown ditch outside the park, and sometimes it is a pain to get them there. The dogs walk closely by my side until we get to the designated area, after one or two trips there, they know where we are going and walk faster to get there. I think it helps also to have a word to let them know it is okay to go.
Like others, I'm not crazy about them peeing or pooing on campsites, or where children play.
I also have x-pen panels to make a large "yard" beside the camper. This is part of our living area, and not a potty spot - the dogs know the difference.
I always pick up, and in 8 years (over 500 nights) of camping I have only seen un-picked-up poo a handful of times.
Happy camping.
