I confirm that “all set” has no naughty or humourous meaning in Ireland. It is likely that the Irish relatives were laughing at something else.
If I said “I’m all set” for another beer, an Irish person might interpret that as meaning “I’m very ready to have another one” or “I’ve prepared myself to have another one”. They might interpret it as an indication of great eagerness for more beer, and so find it funny.
The implication is that you are getting yourself “all set up” to drink more beer, and they might see that as a witty comment by you. I realise that Americans don’t do real wit, particularly self-deprecating irony. * For this reason, you might not see it as humorous.
A great Irishman Oscar Wilde said the English and the Americans were two great nations divided by the same language. English and American should long ago have separated into two languages, like Portugese and Spanish. However, modern communication is dragging them reluctantly back together. I think this is a serious error of judgment.
BTW the above Wilde quote is often attributed to George Bernard Shaw, another Irishman. Don’t waste posting time on this attribution. Oscar got it in print first, although he probably heard it in a Dublin pub. Every Irishman steals good quotes and passes them off as his own - that’s what makes us so articulate.
*(For the uninitiated, irony is what you do to clothes, after you wash them in the cynic.)