I'm a little confused. Is she living in the home now? I thought you asked her to leave and that she was staying with a friend...and preparing for her own place. Did she come back home? If so, would you explain.
You really must work hard not to say and do things in an attempt to get reactions from her. If you told her to leave b/c she was cheating........and then you let her come back home without resolving any issues, do you know the message you gave her? A LBH might as well put an ad in the newspaper that says, "Weak and needy H who will tolerate cheating W.".
I say to apply the same to things like the rings and pictures. If you do take the rings off and put the pictures away......keep it that way untill full reconciliation has occurred. It would not be good to do it......only to turn around to put the rings back onand hang the pictures up again. Reversing the decisions are telling her, "it is okay to have an affair, honey, I don't you worrying about losing me.". On the contrary, she should worry about what this A has cost her. And not only do these wishy-washy actions tell your WAW how weak and undecisive you are, but it tells your family, friends, etc. And talk about confusing kids! So really think it over thoroughly before doing it.
Has your W ever attempted to hurt herself in the past? I usually wonder when people threaten suicide in front of the other person........so as to be rescued. To me, their threats are saying, "Look at me, I have a knife and I am going to slit my wrists....so you better stop me." I don't believe they intend to take their life at all. They have a different outcome in mind. They threaten for other reasons. I think she may have poor coping skils and trying to get certain results........just as you do. However, the experts say to take threaths of suicide seriously. Did you call the police, take her to the hospital, shield the kids, .......what? Did your children witness this? Aside from not knowing her true intent, her behavior is not rational and that should be dealt with. Has she been, or Is she currently under the care of a psychologist?
Just a comment about her resisting a schedule. Implementing a schedule requires a certain amount of stability and responsibility. Where you may see the sensibility in having one, she may see it as pressure.......the means of accountability of her time and whereabouts. I think that may be what she's really fighting against.
You really must stop the R talks! Every time you try to convince your W that the M can be saved, you shoot yourself in the foot. The WAW in an A will not hear what you say. She watches what you do.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!