Does divorce take place when one says to his mother, "I divorce her," as a scare tactic, while his wife is absent, and with no intention of divorce?

Divorce does not occur except with an explicit utterance or an implicit one accompanied by the intention to effectuate it. The phrase "I will divorce her" (أطلقها) in the present tense is considered an implicit, rather than explicit, statement of divorce. The present tense signifies a promise, and divorce does not occur through a promise. Since you did not intend to effectuate a divorce, but rather to instill fear, your wife is not divorced by what you said.