I think because you are in a pop-up camper, things might be a bit different for you than for those of us who have hard sided trailers, 5th wheels and motorhomes. More than likely you don't have an air conditioner. If so and you are camping in hot weather, I would NOT leave the dog in the camper. And most likely you will not be able to leave it chained outside. Often when you check in at some campgrounds, it states on the receipt, do not leave animals unattended; that implies alone in and out of the camper.
We travel with 2 cats and a large standard poodle. The dog goes with us everywhere. If it's too hot to leave him in the car, then we do something that he can do with us. We've found some places allow dogs to participate, especially if I go inside and tell them we have a dog and we don't want to leave him in a hot car, they allow us to bring him in. So, it helps to check with the establishment. One thing you'll want to make sure of is that if you do take your dog in with crowds or other situations where people will be in close proximity to you, is that your dog is well behaved and friendly.
If we find ourselves in a situation where we can't take the dog in and it's a long tour (i.e. Silverton Railroad ride in Colorado) often the campground will recommend a kennel or they may have someone on site to let your dog out and take it for a walk. Having someone come into the camper to let the dog out would be my last resort. I'd be worried something would happen then I'd be responsible.
If it's hot and we plan to leave the animals for several hours, I tell the management that they are inside the motor home and leave them my cell phone number in case something happens. That might work well if the entire campground looses electricity; but if only your site has no power, no one will know.
Traveling with a dog makes things more difficult, but for us, it's worth every bit of inconvenience.
Marsha~