@Judy508
The MO with "add a guest to the itinerary" is to do it before they arrive !!
That cousin's history you probably really don't want to know about, so in a roundabout way you may have been let off lightly. We have this "add guests to your itinerary" as a booking requirement (just for this reason that you have encountered - somebody or a few in the group might have really negative feedback) failing this we manually ID each guest and get them to accept Terms and House Rules and they provide ID. Either way, anonymous guests are no longer anonymous.
Make sure 'he' cancels rather than you cancelling. His preference to not add his cousin is not a reason for you to lose your booking and have your calendar blocked by a potentially troublesome guest.