Is listening to the speaker and the listener's engagement in what is mentioned of conversations between mothers and their daughters, or mothers-in-law and their sons' wives, regarding family problems or the behaviors of sons' wives and the husband's sisters, considered a sin and backbiting for which the listener will be held accountable?

The mentioning by mothers and mothers-in-law to their daughters-in-law of things they dislike is considered prohibited backbiting (gheeba), unless the intention is to advise them or to inform their husbands to prevent them from ill-treatment. You must forbid them from doing so and clarify to them the gravity of backbiting, and strive to reconcile between them.