Even "wife" alone will get you some things you'd probably never want to tell your spouse that you've seen especially since you've asked her, been turned down, and she'd probably prefer not to have that particular discussion again.
While I was waiting for the coffee to kick in this morning and trying to force my brain to cough up the term "troilism" for you, I did a little search myself and found this quite nice article on Nerve that goes into great detail about the culture that has grown up around cuckolding-the-fetish which is not the sort of thing that could have flourished in the pre-Internet age but has certainly come into its own. And aren't we proud?
Actually, I have no problem with it, provided it isn't one of those situations where the man (usually) begs and whines and cajoles and bothers the woman (usually) past the point where it makes sense to do so. Either she won't change her mind or she'll agree to it, meet someone else, and leave the first guy. Either way is OK with me. But neither of these things applies in your case. You're OK. If you can't sleep, try exercise, melatonin, or masturbation.
Andrea is home with the kids and going stir-crazy. Write her a letter! Ask her a question! Send her your tedious e-mail forwards! On second thought, don't do that. Just ask her a question.