Did a divorce occur when the husband said: "If you tell anyone, what is between us will end," knowing that the wife did not know that this was a صيغة طلاق (a formula for divorce), and what are the implications for conjugal relations and having a child after this statement?

The phrase uttered by the husband could be interpreted as a promise of divorce or a conditional statement (ta'liq). Assuming it is a conditional statement, it is a veiled expression (kinaya) from which no divorce results unless the husband intended divorce by it and the condition was breached.

It appears from the question that the wife did not inform anyone after the husband uttered this phrase, so no breach has occurred in the first place. And assuming a breach did occur, the determination of whether there was an intention of divorce or not rests with the husband, as he is most knowledgeable of his own intention.

Therefore, as long as the husband did not intend divorce, no divorce has occurred.