I see this "would" as a sort of combination of hypothetical (describing an imagined situation) and volitional (referring to the other person's volition or will to do it). Different people may have different opinions.
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contrapositionWhat does the second speech mean?"You wouldn't dare!" in that context means, more or less, "You don't have the courage to do that!", the implication being that the speaker may deal out some punishment if it happens. 'would' is used because there is a hypothetical element involved. It's uncertain whether the first person would tell Dad or not.
contraposition'I'll tell Dad.' 'You wouldn't dare!'The second speaker is saying that the first speaker would never have the courage to denounce the second speaker to their father. ‘Would’ implies a hypothesis.