As far as I can see Alan, there is no reason why your scheme should not work, provided all the components do work as intended. However you also do need to look at the risk of failures and how they could adversely affect the caravan. I worked for an test house in the 1990's and I was involved with comparing caravan water systems, both pumps and direct connection systems. when analysing the results, and considering the Failure Effect and Mode Analysis (FEMA) scenarios we came to certain conclusions.
The first concern major FEMA concern was where the pressure reducer failed to regulate the pressure, which allowed full mains water pressure through to caravan's pipe work. When you consider caravan water systems are only designed to withstand about 2.5 Bar, whilst mains pressure (of up to 6 Bar with dynamic pulses of up to 10Bar. If that pressure got passed the regulator you might imagine what havoc it might cause in a caravan. Fortunately such failures were very rare, but I know of about five that occurred between 1990 and 2000 which not only ruined the holiday for the caravanners but also
The second major concern was pressure creep which would occur if debris got trapped in the regulator valve which prevented it from closing completely and allowing a small bypass where the pressure would build up slowly. Generally this would not damage caravan appliances becasue especially the water heaters normally have an excess pressure relief valve which dumps the small flow of high pressure but can't manage a full flow failure as in the first case above.
A problem we noted was that most of the pressure reducing valves could not match the full flow capacities of larger submersible pumps, which can mean high demand water flows such as showers are less powerful.
A collateral problem that can occur with sites where water pressure can be highly variable due to demand caused by several caravans drawing water at the same time, the water flow into your caravan may not be sufficient for your needs. That is not a problem with the direct hose but the sites water supplies.
My personal view is if you want a continual water supply, it is safer to have float valve in your water barrel to accept a mains hose pipe, and to use the barrel as a local reservoir for your submersible pump to deliver the water into the caravan. The pump is simply incapable of over pressurising your water system, and the barrel catters for poor flow from the sites tap.
Happy showers