Get Used to Your Family Being Crazy
Your sister does indeed sound like a piece of work. And I don't doubt that she causes a lot of drama and pain in your family and is probably the source of many of her own problems. But I'm going to play devil's advocate for a minute.
You say she cheated on a "good husband" and then "refused to reconcile with him." I am no fan of infidelity but let's focus for a moment on the "good husband" part. Whenever I see two people break up who were seemingly wonderful for each other, I remind myself that I can't see into their hearts and know what was going on inside all along. The only two people who know everything about their relationship and the emotions and expectations between them are your sister and her ex. He might have seemed like a "good husband" to you but wasn't a good husband for her, without necessarily doing anything wrong except being the wrong person. That is not a justification for cheating, and it does not absolve her of responsibility for any of her other actions, but regardless it sounds like a painful situation.
And the breakdown of a marriage is no fun for anyone, even the most drama-seeking self-destructive train wreck of a person. Yes, even if her actions set it in motion. I know it's a lot easier to feel pity from the comfortable anonymity of my Advice Columnist's chair, but the point I'm getting at is: it sounds like your sister creates a lot of her own problems, but in order to tolerate her complaints, try to summon some pity for her. Sympathy (if you define it as the kind of pity that comes with respect) has to be earned, but pity is free. You might even pity her for the things she isn't aware of -- not just for the things that "happen" to her (which she might have actually caused herself), but also pity her for being incapable of exerting enough self-control, dignity, and self-respect to pull herself out of this mire.
You could get mad at her for being that way -- but getting mad at her hasn't gotten you anywhere, and has just pulled you into her whirlpool of destruction and waste and negativity. You're right that the complainer "wins" in that situation. If you pity her instead, you start to acknowledge that she simply is that way, and you let go of that nagging feeling that you have to get her to change. Instead, when you start getting mad, just remind yourself, "Wow, that is a horrible way to go through life. I'm so glad I found my own, different path."
Real change has to come from inside her. There are times for intervention: if she abuses drugs or alcohol, begins physically harming herself or others, engages in dangerous behavior, or starts bankrupting herself or your parents. But even in these cases where intervention is necessary, the only person who will make her change is herself. You can try your best to remove her from the situation in which she causes harm, but you can't remove the impulses that make her want to wreak havoc on her life and those around her. Only she can do that. Until then, the most you can do is feel very, very sorry for her -- but not for the things she's complaining about. Feel sorry for her for being trapped in her own head.