Is a mother's laughter while speaking of a relative who cursed the religion considered an act of disbelief (kufr), and what is the questioner's duty towards her?

Disbelief does not arise from what was mentioned, as it is possible that the mother's laughter was out of astonishment at the man's words and actions. The jurisprudential rule is that if a word or action admits ninety-nine interpretations of disbelief and one of faith, it should be interpreted as faith, based on the Prophet's (peace and blessings be upon him) saying: "Avert the prescribed punishments from Muslims as much as you can." The questioner should think well of his mother and honor her, and study matters of monotheism and acts of worship with her.