I have a slightly different take on the situation than Mr. Winkle and like him I'm not trying to offend anyone just tender a slightly different viewpoint that's all.
So if I understand it correctly you are in a club spending time with one of the dancers when someone you don't know intercedes on your plans to purchase a lap dance or two or three, etc... I agree with Bullwinkle that this very like would have taken some chutzpah on the kids part but let's think about this a minuet. He obviously knew that you were hanging with the dancer in question and polite or not he asserted himself over you.
He initiated the contact and asked a question "mind if I take her for some fun?" Now in my world the polite thing to do when someone asks you a question is to answer it. Simple right? Which is exactly what you did. Was it the "best" answer? Perhaps not, but it was simple and to the point and it sure doesn't sound to my ears like it was aggressive, rude or inappropriate. Compare it to something like "get lost!" or "what, are you some kind of clown?" or the ubiquitous "fuck off!" and your answer is better represented as what it was...an answer, a simple direct answer.
Ok so try this on in another context. You have a bicycle, a nice new road bike and you are just about to mount it when a young man approaches you and says "mind if I take her for some fun?" What's the proper response? Pick just about anything that you possess at any point in time and ask your self would his politeness and chutzpah make you inclined in any situation to give up what is yours to him simply because he wants it?
The 99% answer is no! Ok so if we have to paint one of you a deficient human which one is it? Think about this the kid had to assume that he was in a superior position than you or he wouldn't have asked you for access to your dancer so he was either "cocky," "clueless" or "belligerent" to a)intrude on your conversation and b)attempt to abscond with the dancer who had been sitting with you for some time. You on the other hand were none of the above you answered the question. You didn't start a fight. You didn't pitch a fit. You didn't overreact.
The kid however was not satisfied with your answer and instead of accepting it and returning to his seat he pressed on. Why? Well my theory is that he lacks respect. Like so many of the ME generation he doesn't understand that when his question got answered he should respect that answer and retire back to his seat to wait his turn. Instead he argued with you. Let me say that again he argued with you. So who has the ego and is forcing the one up one down scenario? He is. He showed a serious lack of respect and frankly I believe that you should have stuck to your guns if for no other reason to reinforce the fact that he can't just barge in and ask (no matter how polite) to take something (or in this case someone) from you.
As far as the dancer's silence goes that is of no significant consequence because if she cared one way or another she would have spoken up. As it was I believe she was going to go with whomever won the contest in a classic "to the victor goes the spoils" scenario. Looking for her to help you make your case was unfortunately for you a PL play (not that you're necessarily pathetic just that your inclination to look to her was a pathetic act IMO).
So what would I have done personally? I don't know if you were standing when he approached or not but I would have stood up and introduced myself with a smile on my face and reaching out to shake his hand. Then I would have joked about my dancer saying something like "Damn she sure is sexy isn't she? I can understand why you would want to have some fun with her and I'll tell you what just as soon as we're done messing around I'll bring her right over to you. Where are you sitting again? Excellent! Well I'll see you in a little while. Take care." and with that I would turn from him, take my dancer friend by the hand and walk away. Nothing more need be said.
I disarm him by owning the conversation and affirming him while at the same time assuming control of the situation. Any argument he puts up get's met with "Ahhh, I see. Of course. Yes I get it, but no, not now. Like I said I'll escort her to your table when we're done. Take care." Disarm with words and a smile on your face. Acknowledge his argument even paraphrase back his points but always end with "no!" and "take care."
Anyway like I said a slightly different take on the situation. Not right. Not wrong. Just different.
Take care ;-)