Question

If a Pokémon with Parental Bond uses a stat-dropping move such as Superpower, will the stat drop occur twice?

Answer 1

Any attack which has a secondary effect (except Secret Power) has the same secondary effect on both strikes (such as Power-Up Punch)

Bulbapedia

A move like Power-Up Punch or Superpower will trigger the secondary effect each time for both hits, but a status move like Curse will trigger the effect only once.

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Answer 2

It does, but the most notable use of that mechanic is that Power-Up Punch also gets its stat boost to occur twice, making it a Swords Dance with some extra damage attached.