The ring thing could have been purely subconcious, but perhaps still meaningful. I agree with Coach 100%. Don't think she isn't noticing you and thinking about you. You don't marry someone, live with them for so long, have kids with them, etc, and not have them be an integral part of your thoughts. You can't just turn that off. In fact, the anger PROVES how much you are in her thoughts.

You're doing exactly the right thing Antlers. Leave her alone, stay dark, in whatever minimal interactions you do have, be nice, and be matter of fact. Not cold, just to the point. It will take a while for her to process through her anger, which she can do now that you're leaving her alone.

I don't know anything for sure of course, but I'll bet at some point, maybe within a month or two, your W will surprise you with a nice comment or pleasant interaction. When this happens, stay cool, respond with the same nice but matter of fact demeanor. Don't show her "Oh thank you thank you thank you!", by your response. You have more power in this and a bigger role than you think you do, but if she perceives that you're expressing that, her anger will come roaring back to protect her. You have to show her that you are no longer going to use your power in your R with her, that you've given it up, so her anger no longer needs to protect her.

You may be thinking "What power do I have?" Just imagine what her response would be if you were to go up to her crying and say "I miss you, please, please come back!" She would probably explode with anger. That anger is her power coming out to meet yours. She doesn't like what she felt she had to do. She's guilty. She's trying to avoid and suppress the guilt. She knows you have the power to throw it right in her face. That's your power she fears, and you need to show her you'll never use it, so she can let go of her anger. If she eventually does initiate a minor nice interaction with you, consider it a test. She'll be watching very carefully for your response.