Were you connected to a public water source or internal pump? If external, did you have a pressure reducer on in the line? Many public water sources, especially in large campgrounds use high pressure to insure water pressure at the end of the run. Many times that pressure is more than the TM plumbing can handle. For a short term fix fill the water tank then use the internal TM pump.
Trace the leak, looking for loose fittings in the plumbing. Had a leak the first night in our new trailer, tightened the ferrule at the back of the outside shower and it went away.
did the leak from the outdoor shower leak into the outdoor storage area? I can't see where the leak is coming from its getting the carpet wet on the bottom edge of the inside wall of both storage areas. I was connected to a campsite water source but did have a pressure valve on the hose.
My trailer's layout is very diff from yours. And tracing the leak can be tough. In my casd it was running across the rear of the trailer under the cabinets and dripping out about 8' from the actual leak.
We also had water getting in through the outer storage doors, but that was only when it was raining and I hadn't closed the door properly.