Hello PaulT
I sympathise with your difficulty, the de-facto type of water heater fitted to touring to-days caravans uses a storage tank. Construction regulations limit the heat input to these devices and as such they will never provide continuous hot-water for showering. Some people still remember the instantaneous wall mounted heaters with the exposed lighting hole. These could provide limited quantities of continuous hot water, but for safety and legal reasons these are outlawed in touring caravans.
The sizes of water heaters are designed in consideration of the physical space available, the additional weight of the water, as well as the ability to supply the heater with water from the portable cold water tanks, and don't forget that waste water has to be taken away.
All these factors tend to limit the size of practical heater tank you can accommodate.
The size of the burner, is limited by the ability to create a heat exchange that complies with legal minimum efficiency within the limited space of a caravan locker. This is considerably more complex than it might seem.
For those with electric heating element, again there are limits created by the available supply to caravans. Although technically 16A (3.5kW) may be available at some sites but much less at others, and of course caravanners will want to use other appliances at the same time as the water heater, so to prevent drawing too much current the size of the heating element is kept down, and the largest available is typically about 1kW.
A domestic electric shower will be rated at a minimum of 8kW and up to 11kW, and if you have experienced one of these you will know that the volume of water can still leave a lot to be desired, so with the much smaller heat input rates of a caravan ( gas about 1kW, & Elec.1 kW) there is no way that you would achieve continuous hot water for a shower.
With a knowledge of these practical limit, hopefully you can see that to expect to have a shower that is as powerful and as long lasting as a domestic one is in reality unreasonable.
Note for Roger L, I would be surprised if the water flow through you caravan shower achieved 12L/min.That figure is probably for the pump with no restrictions such as hoses and head heights.