my sink drain in the shower smells moldy so I have been putting bac out down it. I really don't use that sink its so little. But the shower water also smells moldy when I first turn it on for a few minutes.
Odors from your sink drain and the shower water supply should not be related, so I can't guess what's going on.
Because the plumbing on our trailers frequently sits unused for long periods, I recommend replacing all p-traps with Hepvo valves. They eliminate common p-trap problems caused by both evaporation and freezing. It's a relatively straightforward plumbing project. I did it on my Casita
but an easy job for any plumber.
Also, have you done the standard sanitization process with your water suppy tank and plumbing? That should be an annual must.