I'm not sure about "mandating transparency." I have an urge to say, absolutely no, don't mandate. Just step back and trust that she will conduct her life in the best interest of herself, you, and the kids. If she is hellbent on straying or seeking something outside the marriage, there is probably nothing you can do from stopping that (mutual transparency or not.) But, I think I've read posts on alternate viewpoints on this with someone who has recently cheated... Perhaps others will comment on that.
I'm sorry that this is wearing on you. It must be incredibly tough, and you have a right to feel whatever you feel.
