It sounds great in theory. However, because it's a casual, random senario, lots of things could go wrong. Your wife could get creeped out and not wish to talk to the person, she may try to change the conversation or even move to a different seat.
She may also figure out it's a set up.She is, after all, your wife, and she knows you and what makes you tick. Her intuition may make her suspicious and that could really back fire on you.
All in all, I don't like "set ups", so it would not work if it were me.
I know you are anxious to have her on the "same page" as you. I would give anything for my children to see the WT for what it really is. But I think the only way to get them to come around is to leave things alone.
Continue to be the best husband you possibly can. Don't openly critize the org. or the brothers. Give her no reason to find fault with you. Hopefully, she will, in her own time and way, come to see things clearly. When she does, you will be her "soft place" to fall on and you can come to her rescue.