Not sure of how your RV is built, but I think it's common to have a check valve in the drain line. It prevents backing up grey water from a full tank into the shower. Also known as a backflow preventer. If equipped, there is usually a warning sticker somewhere near the drain warning that tools and drain cleaners may damage the valve. Typically, the valve gets cluttered with hair, especially if there is a long hair user. The clog can be retrieved, but care must be taken to prevent damage. You just can't just jam stuff down the drain. Small, flexible mechanical finger grabbers are what can be used.
Think of the drain check valve as a thin, very flexible rubber duckbill inside the pipe. It allows flow easily in one direction, but when flow wants to reverse, the duckbill closes. Remove the grate from the shower floor. Start with only short penetrations to try and capture the clog. on mine, the check valve was about 10 to 12" downstream from the grate.
Warning, once you get the big wad and start extracting it, it's nasty. You'll need a strong stomach.