Does a divorce oath, uttered by the husband with the words: "If you mention them again, then it is haram and divorce, you are divorced," take effect if the wife mentions her husband's family? And what is your advice to this wife?

The Sharia prohibits reviling the dead, and it appears that the husband intended to prevent mentioning his family negatively, not to prevent mentioning them altogether. A conditional divorce takes effect if the condition upon which it was suspended occurs, according to the majority of scholars, in contrast to Ibn Taymiyyah. Nothing ensues from swearing by "haram and divorce." As for the issue of "I divorce you thrice if you speak to Zayd," a single divorce is binding unless he intended more, due to the non-fulfillment of the condition for enforceability. It is advisable to maintain good companionship, to be deliberate in seeking divorce unless there is clear harm, and to advise the husband to observe prayer.