Difference in religion prevents inheritance. If the second wife's children are non-Muslims like their mother, they do not inherit from their father, neither does their disbelieving mother, who does not inherit from her Muslim husband, according to the saying of the Prophet (peace be upon him),
Neither a disbeliever inherits a Muslim, nor a Muslim a disbeliever.
(Agreed upon by Al-Bukhari and Muslim)
However, if those children or some of them are Muslims, they inherit from their father like the rest of his Muslims heirs. The fact that their mother is a non-Muslim (Part No. 16; Page No. 547) does not prevent them from inheriting from their father. If they were minors, they are treated as if they are Muslims like their father, and so they inherit from him. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.