There should be a check valve in the city water inlet which prevents that from occurring. But if it is stuck, or has been removed by a previous owner, you will get the water issue you mention.
For a temporary fix, plug the city water inlet. For a real solution, you will need to look for the check valve, see if it is there, if so replace it. If not put one in. It should be between the city inlet and the pressure regulating valve, which is a dome like device about 5 inches high and 4 inches around. The check valve will look like a piece of brass pipe, about 2" long, and will have an arrow on it indicating flow direction. This all assumes you can see the parts. On some Airstreams they are buried so deep in the undersides of closets etc, they are almost impossible to even find, say nothing about see or replace.
In the 40 years since your trailer was built, who knows what the previous owners have done. It may be time to think about a newer plumbing replacement system.