Ignore her. Seriously. Live your life and schedule your social engagements as you see fit without considering her at all. Mutual friends, if they know you well at all, aren't going to blame you for what she does and any lies she tells them will be revealed soon enough.
Now, that's easier said than done. You may benefit from seeing a therapist by yourself, just to settle your issues.
As for Rho going spineless in the face of the problem with Signma, that's an issue you need to take up with him and not allow him to avoid it. If he is enabling bad behavior on her part, it is his problem, too, and you can call him on his part in it. You can only decide what you are going to do, however, whatever his response. So decide what course of action you're going to take and take it--he can come along or not.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.