Is the mother considered divorced by the father's saying to her, "My divorce from you is near, or has approached," while he is angry, and is it necessary to renew the marriage contract, and are they living in sin, and are they considered adulterers, and are the children considered children of adultery because of the mother's disbelief and her occasionally cursing God and swearing by other than God?

The father's threat of divorce by saying, "My divorce from you is near," does not constitute a divorce.

A mother's cursing God out of anger is an act of disbelief that expels one from the fold of Islam, unless she is not aware of what she is saying due to the intensity of her anger. If a married woman falls into apostasy and then repents before the expiration of her waiting period (iddah), her marriage remains valid, and this does not affect the lineage of the children.

Swearing by other than Allah is forbidden and is not an act of disbelief that expels one from the fold of Islam, unless the intent is to venerate that by which one swears, as one would venerate Allah.