If she chooses to be dishonest, that's her choice. My W was the same way.
Set your boundaries by saying that if A is something you will not tolerate because you respect her and yourself to much and that you want to have things open between you two.
Whether or not she's seeing someone it'll be her choice to deny or admit to it. It's hard to realize, but we really can't force our S to tell us anything they don't want to. In fact, they'll even recreate history so that you sound like the bad guy.
The only thing you can do is be the better choice. Be the better man. You can't guilt her into staying with you.
M-43 W-40 2D - 9 and 5
Emotion, yet peace. Ignorance, yet knowledge. Passion, yet serenity. Chaos, yet harmony. Death, yet a new life.