Does a man's cessation of spending on his needy relatives, after a dispute with them and their denial of his help, indicate that his spending was not purely for the sake of Allah?

Withholding financial support after mistreatment does not mean that the previous actions were not for the sake of Allah. It remains better to assist needy relatives, even if they are ungrateful. This is evidenced by the story of Abu Bakr Al-Siddiq, may Allah be pleased with him, when he swore he would no longer support Mistah after the latter slandered Aishah. Then Allah Almighty revealed: {And let not those among you who are blessed with graces and wealth swear not to give (any longer) to their kinsmen, the poor, and those who left their homes for Allah’s Cause. Let them pardon and forgive. Do you not wish that Allah should forgive you? And Allah is Oft-Forgiving, Most Merciful.} (An-Nur: 22). So Abu Bakr resumed his financial support to him.