What is the solution for dealing with a sister who spreads false information about the questioner's marital life, causing tension in her relationship with her family and husband, which led to the husband preventing the sister from entering the house, given the questioner's desire to maintain her relationship with her sister, her husband, and her home?

If your sister transmits false information about you and your husband, causing tension in your relationship with your family, then she has combined abuse with injustice. Your husband has the right to prevent her from living with you. If your sister abandons you because you supported your husband in what is right, then she is sinful for doing so. You must advise her and remind her of Allah, and prevent her from injustice; for the Prophet, peace and blessings be upon him, said: "Support your brother whether he is an oppressor or oppressed." Supporting the oppressor means preventing him from his oppression. If you are unable to advise her, then empower someone who has influence over her to advise her. Strive for reconciliation through supplication and by involving people of goodness.