Here is another thought. May be right, or may be wrong, but it strikes me as potentially valid.
Your Sister is calling for attention. The accusation of being a child molester may actually be a cry for help in her own household. It is possible that either she or another member of her household is indeed, molesting children. It may be time for a "down and dirty" one on one with her, telling her that you were deeply offended by her "statements" and are wondering if there is a problem that she needs to discuss with you.
This will now take the conversation into her life, and what may be going on there. If you should decide to share your personal life with her, that will be your choice. Me? I wouldn't.
My first instinct, when reading your opening post was like most of the others. "Get out of the situation". However, after thinking for a few minutes, the alternative, above, speaks more loudly to me.
I wish you all the best in resolving this without destroying your relationship with your sister completely.
