Ok I think we need to slow down here and I can see how your confused. Right now we don't think there is an actual affair so let's table asking her to leave for right now. Also for future reference you can't legally kick here out anyway.
Let's also forget about the boundaries for a minute until we see where you stand.
IMO you have to let her know you know what's going on if it is unacceptable to you and will not be tolerated. If you are going to blow this up and she says "to bad I enjoy it too much to stop" and there is no recourse then don't bring it up. This is where a boundary comes in and you should read up more on boundaries. A boundary is to protect you. I will not live in a marriage where my W posts provocitave pictures of herself on the Internet. What you don't do is give her an ultimatum "I forbid you from posting provocitave pictures of yourself on the internet". You see the difference? The first is protecting your values and the second is trying to control her. Now remember boundaries if crossed need consequences so if you set a boundary you need to implement consequences if crosses which must be substantial or you will lose more credibility and respect which in turn creates less attraction.
IMO creating a fake account is passive aggressive so don't do it. Calmly, look into her eyes and tell her you know what's going on and I would leave the house and go for a drive and let her sit with it.
The number one problem here early on is the WW has lost respect/attraction for the LBS and the LBS desperately trying to save his marriage does desperate and needy thins that actually makes situation worse. If you can avoid that you can stay ahead of the game.