What is the ruling on describing the son's condition as "very cold-blooded" to the extent that the mother "slapped me on my face," and what is the expiation for this act, and what is the ruling on a mother supplicating against her children during an argument?

Slapping the face has multiple facets. Some types are not forbidden, such as Sarah's act of slapping in astonishment. Some are disliked (makruh), such as showing anger or reprimanding an offender. And some are forbidden (haram), such as doing so upon calamities out of impatience. It appears that the questioner's act of slapping was of the disliked type, not the forbidden one. There is no expiation for forbidden slapping; rather, one must repent, seek forgiveness, feel remorse, and resolve not to repeat it. As for supplicating against children, it is forbidden, due to the Prophet's (peace be upon him) saying: "Do not supplicate against yourselves, nor supplicate against your children, nor supplicate against your servants, nor supplicate against your wealth. For you might coincide with a moment when Allah is asked for a bounty, and He grants it to you." Therefore, it is advised not to supplicate against children except for good, and to be gentle in advising them.