I don't think there's anything wrong with it. It's a contraction of Are you not going to go outside?, which is perfectly acceptable; the addition of the negation changes the expectation conveyed by the sentence to imply that the speaker thought the subject was going to go outside. This is useful, and it's as meaningful to ask about an event not occurring as it is to ask about it occurring.
I suspect that your wife's problem is really with the sound of the word "aren't", especially when pronounced as one syllable. (Ahr-ənt sounds passably okay, arnt sounds hickish and suggestive of the dreaded ain't.)