Hi again Annapie
Thanks for answering my questions!
Turkish has already mentioned the BIFF technique to you, which can be very helpful when dealing with hostile communications. We also have some other resources I think you might find helpful.
For dealing with false accusations and to prevent circular arguments, it can be helpful to keep in mind not to J.A.D.E.' as in not Justify, Argue, Defend or Explain:
To avoid circular conversations, don't JADE - Justify, Argue, Defend, or Explain.
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Instead, it is recommended that on any given issue, state your point of view once and once only. Provide any clarifications that are asked for. Anything more than this is likely to be counter productive.
This is not to suggest that you should say nothing at all or back down in an argument. It is critical to take whatever action is necessary so that you, and any children under your care, can live in a safe, happy, healthy and productive environment. It's just not that necessary to talk very much about it.
You are dealing with your sister, but several other family-members are also involved. I think it might also be helpful to look into the so-called Karpman Drama Triangle, you can read more about it here:
Escaping Conflict and the Karpman Drama Triangle