I think this whole thing is quite funny. Someone paid you for a service,
asked for a specific beverage (which was super easy and within means as a
bartender) and you persist to be rude to them, twice? And it was their
birthday Shame on you, this says a great deal about you as an individual.
Was it really too hard to fork over a lime? Your preferences are
irrelevant, a customer ordered something specifically, so give it to them!
It's your job to fulfill their needs and they are paying for a service so
it should be however they want. If you think your preferences are more
important than the people who assist in paying your bills you should not be
in customer service. Also, you wouldn't risk being fined if you correctly
did your job. I think your ego is clouding your judgment my friend.