My advice, let her go.
You can tell her that it looks as if she needs to make a decision, either you or the other guy. Until then, no contact.
Or, you can make the decision for her, meaning, you decide it will not be you. (which is really a decision for you, not her).
Either way, her dishonesty is telling you something. And she does feel guilty for it, which is why she's putting it on you to stop her relationship with the other guy - which of course, she won't even if you tell her not to see him.
Good luck. I hope you find the strength to break up with her, because you could hold higher standards for yourself and those you love.