How can one deal with a mother-in-law who constantly criticizes her sons' wives, speaks ill of them, and spreads rumors, despite their attempts to appease her with gifts and kind words, especially when her abuses extend to include other family members?

After what has been mentioned about treating this woman kindly, fulfilling her requests, and appeasing her, they have nothing left but to await reward from Allah and His assistance against her. For in the Hadith: "If you are as you say, then you are only feeding them hot ashes, and you will continue to have an assistant from Allah against them as long as you remain in that state." Compassion should be shown for the situation of the abusive woman, as she is exposed to Allah’s punishment, as narrated in the Hadith about the woman who harms her neighbors with her tongue: "She is in the Fire." She should be advised and warned about the harms of the tongue by someone whose words she accepts. And the sisters' concern should be Allah's pleasure, not what people say.