Thinking about this, you MUST have a blockage in the toilet's flush valve. Possibly, the trailer's water pump does not supply enough pressure to clear it. You MAY be able to force the blockage through the valve if you hooked your trailer directly to city water without using a pressure regulator/restricter at the hookup. The same would apply for the shower.
Give it a try, but don't leave the trailer hooked up to city water pressure for a prolonged period, because you SHOULD use a pressure regulator with city water.
- Jack