Does divorce occur with the words "she is divorced" said in a context of extreme anger and a desire to prevent the wife from going to a neighbor's house, knowing that the speaker did not intend an actual divorce by that?

If a man reaches a state of anger where he loses awareness, his divorce is not considered valid. If a man makes the divorce of his wife conditional upon her doing something, and she then does what he forbade her from doing, the majority of scholars believe that the divorce takes effect. However, others, like Sheikh Al-Islam Ibn Taymiyyah, are of the opinion that it does not take effect unless he intended to issue the divorce, and not merely to encourage or prohibit.

However, if the wife did what the divorce was conditioned upon under duress, or due to forgetfulness, or out of ignorance, the correct view is that she is not divorced, based on the Almighty's saying: (Our Lord, do not impose blame upon us if we have forgotten or erred.) It has been established that Allah said regarding this supplication: (I have done so). This is the view of the Shafi’i school and the choice of Sheikh Al-Islam Ibn Taymiyyah.

In summary, your wife is not divorced by what happened, and you should exercise forbearance and not use divorce to vent anger or as punishment.