Tell her you know what's going on, but it needs to stop -- now. That it's incredibly disrespectful to you, and to your marriage. Tell her you have no intention of sharing her, and you love her, and you want to fight for your marriage. If she starts to lie to you, put your hand up in the "STOP" position and say "Stop it. We both know you're lying right now, so please stop -- it's very diserspectful."
Do NOT tell her how you know, or reveal any of your sources of intel. Just tell her that you do, and you want to work on your marriage, including any complaints that she has with you, but that you can't do that with a third person in your marriage.
DON'T BEG. Just be businesslike, matter-of-fact, but earnest.
If this is in person, tell her you have to go, and if it's on the phone, make some excuse to end the call. BE BUSY, intense, but not mean or a dikk.