TBS,
Going by what everyone has been saying, and what you say yourself, I think that maybe the best thing would be for you and your wife to go and talk to her HR department together. The situation is fraught with potential pitfalls, and much awkwardness all round, plus your anxiety, plus...
Well, let's face it, this is just a ridiculous situation. It is great that your wife has got a promotion, but she cannot be involved, professionally or personally, with that guy. If she says or does anything negative towards him, he can claim it is being done for revenge, which puts your wife in a position of weakness as his manager. How can she ever discipline him or control him?
I know how important privacy and discretion about this whole thing is to you, but the promotion has pushed the situation to a point where HR really should be made aware of the dynamics involved in the promotion. Your wife is clearly a bright and terrific woman, but she is making herself extremely vulnerable to being charged with bias or prejudice if she does anything to chastise the guy. How can a manager operate in a scenario like that?
If your wife wants to take this promotion, she needs to make a managerial break and that guy. Anything else just is not right, and puts everyone involved in a bad position.
With that in mind, and with your entirely understandable concerns, that is why I think you and your wife should go together and talk to her HR department, to see if something can be changed so that she is not in any way the guy's line manager (even a couple of times removed).