NYGal, what is your gut feeling about your W's interactions with OW? Do you think they are innocent? Is W lying to you to cover up illicit behavior, or is she lying to avoid your reaction? And can you live with lies, whatever the reason?
WH used to lie to me constantly. Some of it was to cover up his shenanigans, but later, I think another part was that it was easier to lie than tell the truth, be questioned, and not believed anyway. I don't have a whole lot of sympathy for that because, hey, if you want people to believe you...don't lie and cheat in the first place...nonetheless...not all lies mean cheating.
In an ideal situation, W would have enough respect for your feelings not to engage in these behaviors that upset you, but that's not happening. But either way, our "protocols" that bring us reassurance are not a panacea. W could seemingly follow your requests down to a perfect science and still find a way to skirt around behind your back if she wanted. Mine did. WH was the epitome of remorse and made it a point to tell me where he was at every point of the day, text me constantly, send me photos of where he was at and who he was with, show me the texts received on his phone...everything. He was still cheating. I would never have known except OW called and told me everything, and then he confessed.
You can't control W no matter what, and even if she did everything you asked, it wouldn't be a guarantee of her honesty. As difficult as it is, either you trust her, or you don't. If you trust her, let it go. If you don't trust her, are you willing to leave, or will you accept anything she does, as long as it means you get to be in a relationship with her?