Hello Hopeful&Doubtful,
That is great you have yourself a good councelor that will help you to become stronger as a person if you can (??). It does such a hit on your self-esteem when you find out your spouse cheated ! (trust me I know) Try to take care of yourself as best you can!
I have a similar situation where my husband has been pursuing other women and has been caught, but still lies about everything. I have caught him in so many changes of stories and inconsistencies it is a joke, yet he maintains that he has not done anything wrong. He had a "just friends" relationship with a young woman in China for a good part of the year he worked over there, but I found notes that indicated it was at least an emotional affair and I suspect much more. I DO know it has hurt our relationship because he has given all of his love energy to her and he has changed with me.
He also does all of that type of behavior, like hiding things..his keys, his computer, his answers to my questions are not answered, etc. We agreed he would become transparent in counceling about all, but he continues to hide everything is what I see.
What I have learned is that it is inappropriate for your spouse to have a "just friends" relationship with the opposite sex unless it's an exceptional circumstance and they accepted as are a part of the family, per say, or you have been platonic friends with this person since childhood, and your mate feels comfortable with it.
My point is it is; when your spouse doesn't become honest it is sad, because it can heal the marriage if they do and you can start to work on rebuilding. I feel so many on this site are so much luckier than I because their spouses have admitted whatever they have done even if it's an emotional envolvement. Trust is everything.
Where you have the children give it time and don't do a knee jerk reaction, keep getting help with this. I hope you have some family support? Best of luck and keep in touch.