I had the same issue with my camper. I would run my inline filter to get rid of debris and chlorine. Because I removed the chlorine, if the water sat in the tank for a few months it would form bacteria. It was so bad if you ran the sink water it smelled like a sewer overflowed. When this would happen, I would add about 2 cups of bleach, fill the tank all the way and run the different faucets until I smelled bleach. After a week I would flush until I could barely smell bleach then change out my filter under the sink (had a separate filter just for kitchen sink). All was fine after that. I had to do this several times over the years before I figured out what was happening.
Bell Brothers customer service was very helpful during this process. I always kept the water tank full in case of emergency. Afterward, I would add some bleach before I stored it.
As for the hot water, I had a 10 gallon (I think) hot water storage tank. Cleared that one out too.
If you go to Lows/Home depo, Look at the stand alone single house filters (large ones) then Google solid block carbon filter. That will rid you of most everything that comes out of a hose and then some. That's what I installed in my trailer and had in my camper. The trailer gets better filtering because of the places I go.
The ones that go inline to your garden hose make good debris and chlorine filters. You can Amazon those for around $15.