Affair Over but Stuck

[Hurt06]

Married 13 years with three kids 6,8, and 12yo girl. Wife had asked for a separation after a move and a job change. I had to attend training and agreed to stay away to let her think about what she wanted. While gone I discovered that she was having an affair. I suspected this all long but she was masterful in lying and deception and it had been going on for months before this. Mostly they have been communicating through prepaid cell, Viber and Skype as these can be erased and hidden more easily. After confronting her she denied but I had already complied the evidence and she eventually admitted what was going on insisting that it had not gotten to sex yet. She tells me later that it was sexual. To top it off the man she is seeing is a divorce attorney! She continues to lie, manipulate, and hide many things and I honestly don't know when she's telling the truth about anything.

Update:

She says affair is over and I can no longer see thats its active going on. Trust but verify and seems to be over. We are seeing counselor but not getting anywhere fast.

She is completely disconnected and says she wants to save the marriage, says she is trying but I see very little effort. Maybe I am too hurt to see progress or I'm grasping at straws. She has ZERO desire to be intimate and is a struggle just to sit in the same room together.

We are sleeping in the same bed but very separated. She never snuggles up or reaches for me in anyway. I'll try and at least place a hand on her back or some part of me touching her hoping for a connection but all is cold. sometimes she even pulls away. I have tried every romantic thing I can dream up and she has no response to anything as far as romance is concerned. She will be intimate but I might as well be by myself its as if she feels like it is her duty and I just feel terrible.

In addition when I have questions she just says she can't remember, and then when confronted with facts.... gets mad.

How do we get passed this stuck area?