I can understand your confusion. You love her and you want her in your life, but at the same time, you should not have to do anything you are uncomfortable with in order to keep someone else happy. It sounds to me like you are not comfortable sharing her, or being with anyone else. Talk to her. Ask her why she feels the need to be in a threesome? and why she feels she is not having any fun? and exactly how a woman would add that fun.... Don't be afraid to ask. If she really does love you, she will be understanding and will want to talk things out with you.
When a person lies and cheats in a relationship, no matter how hard you may try - the trust is gone. You need to rebuild it in order for the relationship to work, and bringing in another woman at this point is not the answer. Your relationship sounds rocky enough now, just think how much more complicated it will be with a third person in the mix.... Only you know what you are comfortable with and what you can accept. However, don't sacrifice your feelings simply because you want to keep your marriage. We cannot control the actions or feelings of another. If she feels the need to lie and cheat, then it sounds to me like there are more issues in the relationship other than those in the bedroom. Perhaps, you may want to try couples counseling. Lies hurt. Cheating hurts. And I may be wrong, but it seems like you have not really dealt with the pain, and instead you are trying to compensate by pleasing her. Please do not ignore your feelings because in the long run, it will only make you miserable, and you may even end up resenting your wife.
As for the sister wife thing, let me just say it is not legal and you may face jail time...taxes are also tricky - it is not exactly practical, but if you think you can live with it and it will make you happy ... again, really think it through, and think too what it would mean if you have children (I am assuming you do not yet have any children).... The same thing with divorce. Really think it through. My best suggestion is before you do anything is to talk to your wife. Be honest with each other and start all over again. Be clear about what you each expect from the other in the marriage, and then decide if that is something you can deliver and handle. I hope this helped... I am here if you want to talk :)