I remember reading your threads before. I liked the thing you did with the wrist band that supposed OM gave your W. I dont know what to say on how to proceed as it really is up to what you can stand. Her lies are probably worse to you than the actual contact with OM - I know that is how I felt. At least my W told me that if we did reconcile that she could not guarantee that she would not return to seeking the attention of OM. That made it an easy decision for me.
You rightly can make demands that she stop contact, but unless she is really commited to you, her habitual nature for attention of OM(en) may control her actions.
I do support you in taking the route of kicking her out if that is the choice you make. She is the one that has broken her vows in marriage.