Is it permissible to take back one's wife after divorcing her irrevocably (three pronouncements), and her committing adultery during the waiting period, if she repents and the husband performs istibra' (ensures she is not pregnant), with the motive of preserving the children and concealing her (sin), despite his not being entirely pleased and accepting of the matter?

A woman divorced three times is not permissible for her first husband until she marries another man in a valid marriage with the intention of permanence, and he has intercourse with her in her vagina, and then he divorces her or dies, and her waiting period ends. This is based on the saying of the Prophet (peace be upon him) to the wife of Rifa'a: "No, not until you taste his 'usailah and he tastes your 'usailah." 'Usailah refers to intercourse. Adultery does not make the woman permissible for her first husband, even if she repents.