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

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 ...

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.