Does a divorce pronounced with the intention of ending a situation and under the wife's threat of a knife take effect, given that there was no real intention of divorce?

If you fear that your wife will carry out her threat with a knife, then you are under duress, and your divorce does not take effect. The Companions (Sahabah) issued a fatwa that the divorce of one under duress does not take effect. This is supported by Ibn al-Qayyim's statement that Imam Ahmad said, in the narration of Abu al-Harith: "If one divorces under duress, the divorce is not binding on him." Al-Shafi'i cited as evidence the Almighty's saying: "Except for him who is compelled [to renounce his religion] while his heart is at peace with faith" (An-Nahl/106), as well as the hadith: "Indeed, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are forced to do."

Shaykh al-Islam stated that the divorce of one under duress does not take effect, and duress occurs through threat or the apprehension of harm to oneself or one's property. However, if you know that your wife will not harm you, or if you can ward off her threat without harm, then you are not under duress, and your divorce takes effect.

To determine the ruling in your specific case, you must refer to the judiciary or reliable scholars.