I'm going to base my opinion on your own reactions.
1) I think that you went for the big guns because of the signals you were reading in the situation at hand. And I'm not going to second-guess you by saying the big guns weren't needed. You believed they were, and you were there.
I confess that I'd have been impatient to end the whole exchange, that I wouldn't have been patient with a few more sentences back and forth. Like you, I'd have wanted an "off switch," the big guns, so to speak.
2) I think that you are posting here because *you* aren't comfortable with the "artillery" you used. I think *you* believe you were too harsh too soon, and it was probably a little uncomfortable after your volley.
So, I think that you don't need to spend any time worrying about whether you were rude, but instead use this as an opportunity to explore some of the other tactics you could use in any similar situation, when one of your guests is making someone else(s) uncomfortable.
To that end:
-you could say, "Rude Guest, come help me in the kitchen," and there say, "I need you to knock this off. It's making everyone uncomfortable."
-you could say, "please stop with this--it's making everyone uncomfortable."
-you could say, "If her drinking makes you so uncomfortable, feel free to leave; I won't keep you."