You have your W in a good spot. Do not cave on kicking her out. Give her a date to be out by. If you want to W back then tough love is in order. She will fight, kick and scream, but she must know that her tactics won't work anymore, only remorse and actions. Her words don't mean anything. The only thing you will settle for is complete transparency, her cancelling her lease and moving back home, her sending a No contact letter, email, or giving the OM a no contact phone call right in front of you. She knows she is guilty because she is jumping thru hoops to try and convince you she wasn't with other man.
And Steve is 100% right, she didn't move out and get another apartment to work on the M.
^^^THIS^^^
She lied straight-up to your face, you told her to get out, then you backed down. Message to her- you're all talk and no action, and she can do whatever she wants without repercussions. I would do just as Joe says and ask her for a move-out date. Yes I know it's going to be very inconvenient, but really there's no "good" time for a separation.
