You cannot nice a cheater out of an affair. You have been too nice and she has played on your weakness.
Ask her to leave.
Go see an attorney and start the divorce process. Have her served publicly. You can always dismiss the divorce late if she starts showing true remorse.
Have your paycheck routed to another new account in your name only. Start dividing finances. Do not allow her access to your wages.
Read and start living the 180. Begin to detach yourself and demonstrate to her you are willing to walk away. Let her see what she will be losing.
Only strong decisive actions by you will allow you to take back the control from her. It may snap her out of the fog or it may not, but at the very least you will start moving in a defined direction. That is better than wallowing in limbo.
You have to be willing to lose your marriage to save it. Do you have the courage to do so?