Have you considered a schluter kerdi system approach?
https://www.schluter.com/schluter-us...roofing/c/SS-W
This is the choice product for high end bathrooms and steam showers. Kerdi matt in particular can be formed to the curves of the trailer if needed.
It's not cheap and you have to know what you are doing on the install but if you want a truly waterproof approach nothing beats it.
While you are at it spend the extra $$ while waterproofing the shower / bathroom floor and lay down a schluter DITRA heat system... nothing beats stepping out of the shower onto a nice warm tile floor
https://www.schluter.com/schluter-us...r-Warming/c/FW
If you want to go old school then you should definitely deploy the red guard regardless of the backing material you choose...