I read a lot of "no reason to distrust a LEO" ... why is that? The LEO has been trained to not trust you, why should you trust them? In my book, trust is something earned, not given. Although, distrust does not mean disrespect. Just because I don't trust cops, doesn't mean I would be disrespectful.
Refusing a search on the grounds of no warrant, I wonder how that holds up since your "home" is also a motor vehicle (is that different for a towed trailer?)
An automobile can be easily searched one of two ways. First, depending how badly the cop wants to search and you say not without a warrant, they say fine. they'll tell you that you (driver) will be detained (not arrested), and they will call a tow truck for your ride. They'll say once we get a warrant we'll search it... and if the warrant is declined, here's the bill for towing your car to our impound lot... you're not getting your ride back until it's done being processed at the end of the week. You can be detained 48-72 hours (depending on the local laws) without being charged or arrested.
Alternately, they'll call a K9, which is trained to circle the ride a few times, and then "hit" pretty much wherever the handler tells it to. Then the driver will be arrested and they tow your ride, search it, no need for a warrant now, the k9 gave them probable cause. Now you get to go through booking, mug-shots, finger prints and you're not getting bail until you've been arraigned, which could take a few days to a week. You'll get a bill for your public defender, a bill for towing your ride, and a bill for however many nights you spent in lock-up.
How this works with a motorhome that is someone's residence, that would be interesting to read about, actual rulings from a judge, not hearsay or speculation.