To answer your specific question, the tongue weight of the trailer is subtracted from the available payload of the motorhome. Since the hitch is in back of the rear axle, in many cases by a good bit, it will tend to shift weight from the front axle to the rear axle(s) due to its leverage, meaning the weight on the rear axle will increase by more than the trailer weight. You could in theory compensate for this with a weight distributing hitch, but that is not commonly done with motorhomes.
There are several limits that should be observed when towing. The GCWR (gross combined weight rating) is the maximum total weight of the motorhome and trailer combined. The GVWR (gross vehicle weight rating) is the maximum weight on the motorhome, including your stuff and the tongue weight. The GAWR (gross axle weight rating) is for each individual axle, which means it's wise to weigh each one separately. There are also hitch tow weight ratings and hitch tongue weight ratings, and of course maximums for the trailer itself and its components.