Actually the trick is to be clear about this up front. Not done often, as most of us at some point in our (starting) careers were just too afraid of not getting a gig (or worse, lose one) by speaking up.
Every game has rules. Also true for DJ-ing. The best way to play a game is to make sure all principal players know the rules.
I have done a lot (and still do a few) corporate functions, weddings and birthday/anniversary parties. And I make it a point in advance that I will take their wishes into account if and when appropriate. And whether it is or isn’t appropriate is totally up to my discretion. If they don’t have the faith in me to perform at a function/event/party without the input of the organizer, then I will tell them politely that I decline the job to avoid mutual disappointment. It has happened a few times over the years, but funnily enough I only ever lost one gig due to it. All the other times they back-pedaled and said they understood and no, they wouldn’t interfere in the creative process.
Clearly you give room (in advance) to wishes the organizer might have and you try to take that into account when preparing for a gig. I personally limit it to a handful of personal favorites and maybe a few genres that are favored.
But it’s pretty shitty if this happens on your first gig.
For what it is worth, the lady was wrong in her actions (and in my opinion in getting drunk, if you organize a function you stay sober – but that’s a different story).
What you fail to mention is how the rest of the audience reacted to your performance and if you enjoyed yourself (apart from the lady bitching obviously). You only ever get one first gig.
From personal experience, more often than not the next time you talk to people like this after they have sobered up they have forgotten about it all and just remember having a good time. People can be funny like that.
Whatever you do, don’t let it get to you. Keep on spinning!