At the risk of being chicken little First I would disconnect the battery charger before any more sniffing around.
If its the battery(s) that rotten egg smell is hydrogen gas. Hydrogen gas is explosive. It is also corrosive both to metal and human body parts, dont take a deep breadth when opening the battery compartment.
If its enough to seep into camper I would think you have a problem. Overcharging because of faulty (or by design) battery minder can cause batteries to boil, (creating gas). Removing said charger batteries may be ok if its just charger continuously charging fully charged battery.
Or battery can go bad- hooked to a charger that doesn't know the difference between needing a charge or shorted cell.
Sewage - dead mice - stinky stink can be dealt with but first verify it ISN'T or is the batteries. If battery hot and seriously out-gassing after removing charge source let it cool down before doing anything. Slightest spark can cause explosion. Did I mention hydrogen gas is explosive?
Once batteries cool check. Bad battery, voltage usually will fall pretty quickly. Or take somewhere and have tested. I had a battery loose a cell- noted solar was sending quite a few amps to batteries not in use- opened the battery compartment about burnt my sinuses out, I ended up replacing both batteries.
Hopefully you just left a melon in the fridge,