As Hutch has said trying to remotely diagnose a problem like this can sometimes be very difficult as we don't necessarily have the same frames of reference when it comes to describing technical issues.
But reading the thread again, I'm baffled by your description of the sounds of the pump. You say the pump will start normally, but then the flow reduces and the pump is "still whirring" I must admit that is typical description of a pump that has got air into it and is cavitating, but the remaining posts seem to discount that so I'm intrigued by what you call "still whirring" .
Can you confirm if you mean the noise the pump makes when it is " whirring" is the same as when water is being delivered or does the noise it makes appear to speed up or slow down? That might be an important indicator.
You seem to understand that the submersible pump needs to be fully submersed to operate, can you confirm the pump is touching the bottom of the water barrel, and it has remained submerged? If the pump momentarily has no water, it will loose its ability to pump and it will apparently sound as though it has sped up.
If the pump appears to slow down (and assuming the supply voltage has not changed) then that indicates there is greater load on the impeller and that will happen if the flow has become more constricted or blocked.
Can you confirm the supply voltage at the battery/power supply is not dropping below 11V when the pump is operating?
Even with answers to the three questions, I'm not sure we are going to be able to accurately remotely diagnose your difficulty. You seem to be unsure of what you have in the caravan, and guessing is not an effective way to reliably solve such things.
It's getting to the point where it will certainly be quicker and more likely to find a resolution if you were to engage the services of a mobile caravan technician to attend the caravan, not only will it resolve the problem you would get your system full identified so you could hopefully find the necessary instruction books, but the techie would probably be able to explain and show you how to use it.