Does divorce occur in the aforementioned scenarios, with the wife requesting it to spite the husband, and the husband uttering it in a state of extreme anger, and then again calmly with the intention of intimidation?

The marital relationship should be preserved, due to the firm covenant made between the spouses and what Allah has placed between them of affection, mercy, and tranquility. It is not permissible for the wife to seek a divorce except for an urgent need or necessity, due to the severe warning from the Lawgiver to whoever seeks divorce without cause, as the Prophet, peace and blessings be upon him, said: "Any woman who asks her husband for divorce without cause, the scent of Paradise will be forbidden to her."

The explicit pronouncement of divorce by the husband is effective, and his anger is not considered [an impediment to its effectiveness] unless it reaches the point of unconsciousness. If the husband repeats the word of divorce with the intention of emphasis, then only one divorce occurs, and then the second divorce is counted against him, making it two divorces. He may reconcile with his wife before the expiration of her waiting period without a new contract, by word or action with intention.

They both must be careful about uttering the word of divorce, whether in seriousness or jest, because only one divorce remains, after which the wife becomes irrevocably divorced from him until she marries another husband.