I don't think it can be stated enough: tell her the truth! You may also want to consider which relationship has more importance: your relationship with your wife, or your relationship with CD'ing. My SO hasn't always been so encouraging and accepting, and still has her moments, but my relationship with my SO by far has priority over everything, and I have told her many a time that I would drop everything for her, all she has to do is ask.
Good luck, though.