Does divorce occur if the husband divorces his wife under duress, without any intention of divorce, thinking that this would appease his wife?

A wife's request for divorce and her insistence on it does not constitute a valid coercion that prevents the divorce from occurring. Valid coercion occurs when there is a strong presumption of severe harm, such as death or physical abuse. Coercion requires certain conditions, including: the coercer's ability [to carry out the threat], a strong presumption that the threatened harm will occur, and the harm being significant, such as death, severe beating, or prolonged imprisonment. Therefore, if the husband utters a clear statement of divorce willingly, his divorce has taken place, and he may take his wife back if it was less than three divorces and before her waiting period (iddah) expires.