There isn't an "easy" way, sorry.
You could just cap the line and hook up a handheld to the sink if you really just need to shower in the unit. Once you get that faucet out you will be well on your way to repairing the floor rot at the rear of the trailer.
So yes, you do need to remove the panel in front of it to get access for replacement. You might be able to use one of those vibrating saws to cut away just enough plastic to fit another mixing valve. Then you could fashion a patch to go over the hole. Is all the rest of your plumbing working well? Pex is your friend
Good luck....
John