Is it a sin to tell my friend what a woman said about her and her daughter, which is backbiting, and what is the ruling on that?

Advising and enjoining one another to truth, and defending the honor of Muslims, are among the most emphasized legitimate demands. It would have been more appropriate for you to advise the sister with wisdom and good admonition, explaining the danger of slandering the honor of Muslims, and defending the honor of those accused, based on the hadith (definition): "Whoever defends the honor of his brother, Allah will avert the Fire from his face on the Day of Resurrection." Informing your friend about the other friend's words falls under the category of forbidden backbiting (namimah (definition)), unless it is for a benefit or to avert a harm. It would have been more appropriate for you to seek the help of your husband or one of your mahrams to speak with the woman's husband to warn her, and to seek the help of your good friends to try and convince her. You should also encourage her to read beneficial materials, memorize the Qur'an, and learn beneficial sciences, so that you occupy her time with what is beneficial.