Will a divorce occur if the husband says to his wife: "By God, if you had done the thing I detest, I would not have kept you for a single second under my responsibility (on my 'ismah)," if she had indeed done that thing? And is she obliged to inform him of that, despite her fear of explicit divorce being pronounced?

The husband's statement, "I would not have kept you under my [marital] responsibility," is a euphemism that could imply divorce or other meanings. Assuming he intended divorce, its wording is not a suspension of divorce but rather an announcement that he would divorce his wife if he knew she had committed an act he disliked. Therefore, the woman is not divorced by this statement, and she is not obliged to inform her husband of what she did; in fact, it is impermissible for her to inform him if it was an act of disobedience to Allah. She must obey him in what is good, and if she disobeys, she must repent.