Is the husband's refusal to divorce his wife after the legitimate marriage contract, based on her request without harm, while he knows that a third party incited her to do so, considered a sin and an burden upon him, and what is the "harm" that entitles a woman to request a divorce?

A wife is not permitted to seek a divorce unless there is a legitimate Shar'i reason. Her mere love for another person does not make it permissible for her to do so; rather, it is a grave sin that incurs Allah's wrath. The wife must sever her relationship with this person immediately. The fatwa (definition) given to you by a shaykh, stating that it is obligatory to divorce her, is incorrect. This person who is corrupting your wife is committing a grave sin, and if he does not desist, you should report him to the responsible authorities.