Will a person be rewarded for his patience and endurance with his mother who backbites and mocks Muslims?

Striving against oneself to be dutiful to one's mother, despite her bad deeds, will be rewarded. So, be keen to honor her, treat her kindly, pray for her guidance, and advise her gently. Keep her from speaking about others by studying hadiths of encouragement and deterrence, stories of the prophets, biographies of the women of the Salaf, and useful tapes about guarding the tongue and warning against backbiting and mockery.