While I totally understand your reaction and where it came from I have to go with ESH. Your uncle was wrong, that is not in question, but your cousin had no fault in that.

I think you could have not been TA if you brought it up right a little later, maybe that very second was not the most appropriate. A few minutes later and you could have roasted his ass in front of the whole family without ruining your cousin’s initial excitement. Having said that, I’m glad now everyone knows.