If you know she is flat out lying to you, how can you trust anything she is saying to you in regards to R? It sounds like you are believing what you want to believe, despite contrary evidence staring you in the face.
If she really is interested in R, she needs to go No-contact with the OM immediately. And she needs to be transparent. You should not need to spy on her facebook page, you should look at it to see that she is staying true to her course.
Stop letting her make all the decisions. You are a full partner and need to step up and lead here. Don't allow her to set the course of your marriage because she is still trying to cake-eat. She's got you for the day-to-day stuff and the OM for her emotional/sexual needs. Is that a satisfying setup for you?