Hi, I’ve come across explanations online regarding a child being punished for the sins of their father in Tanach. It’s explained that the child was likely continuing the same morals of his father in sinning. But what about in the case of David’s unborn baby that was punished on account of David’s sin of killing Uriah and taking his wife? Surely, one cannot posit the same argument. It seems here an unborn baby is dying due to the sin of his father without any possible chance of continuing the immoralities of his father.

ב"ה Shalom Your point is absolutely valid, and basically it is the answer to your own question. That is to say, that when do we apply the rule when the children adopt the actions of their ancestors as their own they are then held accountable for the sins of the fathers ? That is when they are at an age to be held responsible for their actions. But when the children are small or even unborn as in the case of David Hamelech's child, the small children are caught up because of the sins of the fathers. Just for example, see The Gemara in Shabbat 32b, which says that due to unfulfilled vows children die. (See קובץ שיטות חד מקמאי מסכת שבת) So may Hashem keep us and our children from all evil. Besorot Tovot