Most Forest River products do have the bathroom sink draining into the black tank. The idea is to have more water going in there than solid 'stuff', or so my dealer said. (What's funny is that even the solid stuff is mostly water anyway and left alone would turn into liquid anyway.)
I assume you have a shower grey tank, just pour the chemical in the drain for the shower.
2006 Flagstaff 831RLSS Travel Trailer
2007 Chevy 2500HD 'Classic' with the Duramax engine.
Converting a 1956 GMC PD4501 Scenicruiser, ex Greyhound into a motor home.