Well, intake, we digress here a bit. But, though a motorhome might be considered a home for tax purposes, it's a motor vehicle in the eyes of the police while on the road. At a nearby park, it would be on public land. Therefore, subject to the same laws people in cars are.
For the benefit of those that believe this was an illegal search and detention, I offer:
Delaware v. Prouse
However, the key words in that case were "capricious detention." We'll see if any plaintiff's attorney takes that road.
And for Rick, here is what the above case indicated about spot checks, road blocks, etc.,
"(d) The holding in this case does not preclude Delaware or other States from developing methods for spot checks that involve less intrusion or that do not involve the unconstrained exercise of discretion. Questioning of all oncoming traffic at roadblock-type stops is one possible alternative."
See the above link.