Transparency has nothing to do with you controlling her actions. She can choose to do whatever she wants. Transparency is her allowing you to "see". If she has nothing to hide, then why the need for secrecrecy?
People have their own opinions about trust. Ultimately, it is up to you, whether or not you feel you can trust her. I have seen LBH's say they choose to trust their WW......although she's made absolutely no move toward doing what is necessary to help the MR heal. Personally, I see it as very arrogant on the WW's part, to expect her betrayed H to trust her when she has put no effort into demonstrating her faithfulness. Not only does your WW think you should just trust her, she won't even commit to working on the MR. If she goes into MC with that type of attitude, what are the chances?
As I've previously explained, if she wants to carry on an A, she can easily find a way. That is not the point behind transparency, IMHO. Transparency is about her willingly opening herself for you to see that she has no hidden agenda. That's all it is. It helps to stomp out the secrecy and suspicions. If she cannot allow you to see that much.......then do you really want a MR with her? That is an answer you have to decide. I'm certainly not going to fall out with you, if that's what you decide. But I will tell you this much......I don't recall a successful restoration in the relationship, where there was no transparency......not when there had been an A. Maybe one will come to mind, but ATM, I can't think of one.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!