Are the two words "تتطلق" (she gets divorced) and "نُطلّق" (we divorce) that were spoken during the father's conversation with his son about divorcing the son's wife considered to be merely narration, such that no divorce takes place, or does divorce take place by them, or by one of them, and what is the ruling if the speaker does not remember?

A wife is not permitted to seek a divorce without a valid Shar’i (Islamic legal) excuse, and her family is not allowed to pressure the husband into divorce.

Regarding the two phrases mentioned, if it is not certain who uttered them—whether it was the husband or his father—then no divorce occurs as a result of them. This is because the default is the continuation of the marital bond, and doubt prevents the occurrence of divorce.