Rotten egg smell is caused by dissolved hydrogen sulfide. It often occurs when organic matter breaks down in water. You may have sulfur in your tap water and this can combine with the hydrogen in your water, especially if the water is "old".
You also have hydrogen sulfide in sewer gas which is emitted by your black tank and is normally vented high up by the "stink pipe" in your trailer. If you have a leak or bad connection in that vent pipe, you could be smelling the gas from that.
The anode in a hot water tank is not there to prevent hydrogen sulfide. It is used to prevent galvanic corrosion in the tank, which is not really a problem in a trailer tank since it is not in constant use like a household hot water tank is. You should open the nylon drain plug and empty the hot water tank whenever you are not going to be using the trailer for any length of time. Once drained, replace the plug loosely to keep bugs out.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH, Progressive Dynamics Converter, Fan-Tastic Fan
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew