Well, look, I'm a 20-year-old girl, so I don't know anything about parenting, but I do know what it's like to be a teenage girl. If I was your daughter, I'd be rather embarrassed: you treated her like a child in front of a boy she wanted to impress. There's a time and a place to tell a teenage girl off, and that time and place is NOT in front of her boyfriend. From her point of view, the reason probably seemed petty: she didn't do what you said, but it didn't really hurt anyone. Your wife was awake and didn't mind being bothered. So you were "wrong" to give your order in the first place. While she ought to have had more respect for what you said, you needn't have humiliated her by telling her off in front of a boy she liked. Your wife probably understood that and thought it wasn't worth the argument you'd get if you didn't let her go to the carnival.

Honestly, I don't know why you feel the need to seek validation for your emotions. Feel however you feel about whatever happened. But I really think this is a rather small thing that I wouldn't dwell on too much. Your daughter just wanted to go out, your wife was tired and didn't feel like arguing, and you were trying just a little too hard to put your daughter in her place in front of a guy she liked. From what you said, I don't think it's really an attack on your parental authority.