"Me and my wife" or "my wife and me"

Which is correct: me and my wife or my wife and me? The sentence in which this is used is

Ms. Smith informed me and my wife that she was afraid of being accosted.

According to Grammar Girl, it's "a rule of politeness" to put yourself last in the list:

Ms. Smith informed my wife and me that...

General Writing and Grammar help concurs, but does not offer any additional authorities on the matter.

The Merriam-Webster Learner's Dictionary offers the same advice: third-person, then second-person, finally first-person pronouns for general usage; mixing up the order is not necessarily rude, but can serve to emphasize the role of the speaker in the action, or as a cue that the speaker is talking informally or is less-educated.

Both are correct, you can use any of them. They don't even bear any difference. The same would apply to:

I and my wife were informed that ...

versus

My wife and I were informed that ...