Typically when one of your 12-VDC fuses has the red light ON, then that is an indication that the fuse is bad, so I would replace it regardless and get that red light to go out.
Next, when an inline fuse is warm or hot to the touch, your appliance is drawing a significant amount of current. Most appliances with their own fuses will be designed so that the inline fuse does NOT get HOT.
So, your camper has a COACH battery that would be kept properly charged by a CONVERTER, but if you are not plugged into 110-VAC then the Converter does not operate. The reason I mention this is because your COACh battery may not be holding a charge and the 12-VDC battery voltage could be dropped to a level where your appliance is not operating efficiently and will try to draw more current than normal.
So, check that battery and make sure it is good, that it has water in it, and its voltage stays a steady 13.5-VDC across the battery's terminals.