If the room next door is disturbing the peace and quiet, then calling the hotel staff to tell the room next door to stop disturbing the peace and quiet is quite normal. Hotel staff ought to be well versed in how to appropriately resolve noise issues emanating from one room into another that is disturbing the peace. If that is considered a failure, then deal with corporate/Hyatt and they'll work with the GM in such matters.

The "security" implications of sexual activity -- paid or otherwise -- pale in comparison to the health implications, but I'm certainly not one to invite state authorities to interfere in the sexual activities of consenting adults in a room and have great reservations about a hotel interfering in the sexual habits of consenting adults. To me, the primary issue is that of one room's guest(s) being disturbed by the noise created by another room's guest(s).