If your trailer is like most others with carpet, the entire floor was covered with linoleum (if indeed your trailer has any linoleum) and the water may be traveling under the linoleum instead of the carpet. If your carpet is laid directly to the flooring, then I have no guess how the water is getting from A to B.
Sometimes these type of problems do not have the logical first thought answer--you may just have to quit showering....
Have you tried running the shower with cold water only, wait to see if the leak shows up? Then hot only, to see what happens? This might also give you an indication if weight on the shower floor is part of the problem, or if it actually is tied to the hot or cold only.
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired