Water pump to regulate high pressure?

Hi,
I'm looking for a water pump to pump water from a storage tank at a constant 3 bar pressure.
It's at a campsite I run that's at the bottom of a long, steep hill. We struggle with very high and often fluctuating (around 7 bar) water pressure, which wreaks havoc with our water heaters.
I've just installed a 50 gallon loft tank on a raised platform. I believe I need a 240V, 3 bar pump that will automatically kick in whenever someone turns on a tap, shower, or when toilet cisterns need to fill, but then stop as soon as they stop calling for water.
The pump needs to feed both cold taps and also 3 water heaters (2 x LPG and 1 x electric) that will collectively supply hot water to 2 showers and 3 sinks. (These will very rarely all be calling for water simultaneously.)
Would any 3 bar shower pump work, or do I need some other kind of specialist pump instead?
I've installed a second hand Watermill 3 bar pump, but it doesn't seem to be working properly, so think I need to buy a new one.
I've noticed that even with the water pump turned off, we're still getting very high pressure through the cold taps, suggesting that even with the tank there, it's still pushing the water through hard. I believe most pumps are designed to boost pressure. I need one that will reduce and regulate pressure to 3 bar, rather than boost it up to 3 bar...
Has anyone else encountered and successfully fixed similar water pressure issues in this same way before? Any tips?

Is it possible to fit a pressure reducing valve to each mains inlet to where they are required? If you are supplying drinking water then a storage cistern is a big no no. If not then a much larger cistern will be required and a pressure switch fitted to the supply pipe to the outlets which will automatically turn on and turn off the water. If it is supplying drinking water then pressure reducers where required is the way to go.

How high is the hill 40m as that will add 4 bar eg if the tank is at the top of the hill and water heater is at the bottom

Tbh you won’t need any pump if yes to the above