If she is at peace with this decision, then why does she care who knows about it? There are only 2 reasons I see for "keeping it quiet." One is if you are both really unsure and are working on it. Especially if you don't want the "rumor mill" to get back to your kids. And two is if she just doesn't want people from church "hassling her" because her mind is already made up.
The first reason requires close cooperation and telling a very limited number of people. And not, for instance, filing papers at the courthouse (public record).
I never took you for the vengeful type, and I'm not suggesting you try to "punish" or "shame" her. But you do need to make clear to her that you are not going to shield her from the normal consequences of divorce. Such as: extended legal disputes, lowered standard of living, longer work hours, limited parenting time, and disapproving friends and family.
When I went for limited (not life-time) alimony, XW complained that I had promised to "take care of her" forever. I had to explain that I was willing to do that for my wife, but if she didn't want to be my wife, then she could take what the court decided. Your W isn't asking for alimony, but she is asking you to take care of her, to set her up in her own home and watch the girls whenever she decides to work and generally make this easy. Not your job anymore.
