Does divorce occur if the wife tried to replace the word "divorced" with the word "school" in her statement "she is forty-four years old," so she uttered the "m" and perhaps the "d," then stopped and recalled the word "divorced" in her mind, so she feared that she might have uttered it?

What you mentioned does not constitute a divorce. A person afflicted with obsessive-compulsive disorder (waswas) does not incur divorce, even if he utters its لفظ (pronouncement) explicitly, unless he truly intends and wills it in a state of tranquility and stability. This is because he is often overwhelmed in most of his states. The mere internal monologue of a person with waswas about divorce does not constitute divorce, nor does his doubt about having uttered it. Ibn Uthaymeen advised the person with waswas not to pay attention to divorce-related whisperings, and to seek refuge in Allah from the accursed Satan, emphasizing that divorce does not occur due to waswas.