Unless you love to follow every last rule, this is what we do:
We carry two maybe 2 gal identical buckets. We put car washing soap into one bucket and fresh water into the other. We use a soft brush screwed into 4' pole. I dip the pole into the soapy bucket and complete a short portion of the trailer. Then I slop fresh water on to rinse that area. As soon as the fresh water bucket is running low, my wife refills it. On we go, constantly refilling the fresh water bucket as needed. The job goes fast. We carry older bath towels to dry.
We've never had anyone complain at any place. We work so fast, they have very little opportunity to complain and stop us. To discourage squabbling, we usually start around 6 pm after most site workers are gone.
No neighbors have ever said a word over the last 5 yrs of doing this. I think the reason they don't want you "washing" your trailer is because they are worried about complaints due to overspray. With my technique, you gotta really be searching for trouble if you complain. But, as I say, no one has ever said a word and we've done this at commercial parks, national parks and national forest.