Wow. what a terrible situation. I can't believe the previous owner put up with this and then conveniently forgot to tell you.
The fix will not be easy, but you obviously need to re-route the shower drain discharge to the gray water. The hardest part will be trying to work under the shower pan -- there is no easy way to get under there.
Here is a suggestion: when I had a leaky shower drain on my old T-139, I cut a rectangular access panel out of the woodwork enclosing the shower pan, using an oscillating multi-tool. After repairing the leak, I then covered the hole with a piece of plywood and then stained it to match the existing paneling. Not beautiful, but adequate.
One more caution -- when working way under the shower pan with your arms extended, watch out for sharp staples sticking out here and there. When I say "watch out," I don't mean it literally, since you can't see what you are doing when your arms are groping around in the dark. I actually mean "be careful."
Please don't ask how I know this.
One more thought -- I think that Drano may be too harsh for the plastics used in RV plumbing. I am not sure I am right about this, though.
2012 Fun Finder X-139 "Boondock Style" (axle-flipped and extra insulation)
2013 Toyota Tacoma Off-Road (semi-beefy tires and components)