Is it permissible to inform the husband of his wife's infidelity and her causing his sister's pregnancy, given that he has a daughter with her?

The duty is to advise the woman and conceal her fault. If she repents and desists, then all is well. Otherwise, her husband should be informed so that he may take deterrent measures. Espionage is permissible when there is strong suspicion that a reprehensible act, such as adultery or murder, is ongoing, in order to prevent the loss of something that cannot be recovered. As for one who has committed adultery, they must repent and conceal their sin, for open declaration combines two sins.