Is the husband's saying to his wife, "Be quiet, or else I'll divorce you," considered a divorce, especially since it was intended as a threat and was not followed by a divorce? And is the accidental death of a son considered a punishment?

Your statement to your wife, "Be quiet, or I will divorce you," does not constitute a divorce; rather, it is a threat and a warning, and your wife remains under your marital bond. The death of your son is a divine decree from Allah, for every soul has a limited term, as Allah Almighty said: "And never will Allah delay a soul when its time has come" and "And when their time comes, they will not remain an hour behind or precede [it]." As for whether that is a punishment from Allah, this is among the unseen matters that only Allah knows, and the believer's entire affair is good.