I think we have misunderstood your problem, possibly due to incorrect terminology. Based on your description of of the adjustment wheel you are actually referring to the Pressure Switch. A PRV stands for Pressure Relief Valve which water heaters do have, as I described above.
However your more detailed description of the symptoms does suggest a possible cause for the Pressure Switch to flutter. The fact you have had to replace the pressure switch suggests the system may have been damaged by frost.
Its essential the water system is fully drained down if the caravan is to be stored and there is a risk of frost, as any remaining water lying in valves and in the heater will freeze and expand as it gets colder. This can damage the internal workings of the pressure switch, and also the Non Return Valve on the cold inlet to water the heater .
The expanding ice can unseat and distort the "O ring seals inside the NRV jamming it partly but not fully open. This results in a restricted flow of cold water into the heater, which means the pressure in the cold pipe work might rise enough to trip the pressure switch, but the heater's tank has not been fully filled. So as cold water continues to fill the tank it reduces the pressure in the pipework enough to cause the pump to turn on again. This may happen several times until the pressure in the hot tank has equalised with the cold pipework.
When this happens its common to notice the hot flow through the taps is poor compared to the cold, and some times uses notice when they turn on the cold tap, the water flows for a second or so before the pump turns on, and some even report having a pulse of warm water through the cold tap before the pump starts. The compromised NRV fails to lock the hot water in the heater and as it expands as it heats some will push back through the NRV into the cold pipe work, as will the greater pressure of the hot water thus adding pressure to the cold water for a moment as the tap is opened.
SOme times the NRV on the heaters input can be dismantled and re assembeled and it may work again, but on other occasions it may need to replaced.

p.s The originals were white plastic