An apology is easier to put on paper—you're calmer, you choose better words and take more care with what you say. Apologize very clearly and don't use weasel phrases like "I'm sorry if you were upset by X." Instead say, "I really appreciate your patience as I learn to stop drinking." Then bring it around to them—"It was an absolutely lovely party, at least the first half that I remember." Finish with something appreciative about them, such as "thanks for putting up with me."