Lan, at this point I dont understand why you dont tell her what you know and how much. It sounds to me -and forgive me if I got this wrong- there is no doubt left about what was going on with the IM guy. And I know from own experience that she will not admit anything unless you havd some hard proof and then even maybe not.
BUT, since it sounds that this may be your last effort, things should be out in the open and your possible effort thru MC or not should not start based on lies again. Your wife strikes me as a person that will not stop if she thinks she can get away with it. Committement is the key here and when she keeps lying, I dont see her committing to a an effort honestly. It sounds like she doing some "damage control" while trying to figure out what you know.
Also, I agree, MC is difficult when both people arent really ready to go thru it and a bad councelor can bring tension and NOT give you solutions. Be careful with that. xxx K