Campsite

[Lazaros]

I just ended up building the campsite - knowing my luck, Rodney decided to call it his home now, and he doesn‘t wanna leave. Talking to him leads to the dialogue option of: inviting him to stay at my town or inviting him to stay at my town, which I really don‘t want. Any chance he‘ll go away or do I really have to ask him to become a resident of my town?

 

[Khaelis]

I think they stay longer than a day, should go away eventually.

 

[Lazaros]

I wish that was the case. :/
Tried around for a week ingame, Rodney never went away and moving the campsite doesn‘t evict him either. So, Animal Crossing really is forcing you to take in the first camper you get, unfortunately.