What should a man do who married a widow under the guardianship of her son, then divorced her to please his first wife who asked for her return, then asked for her divorce again? And should the second wife inform her family, or should the man show his first wife that he divorced the second and secretly resume his marriage to her?

There is no impediment to giving the wife the choice between informing her family of her marriage or keeping it a secret. It is permissible for the husband to make it appear to his first wife that he has divorced the second, either by informing her of the first divorce or by divorcing her with another pronouncement and then taking her back without the first wife's knowledge, while considering the consequences and weighing the benefits and harms to choose what is best.