No, it's still only one Pokemon using one move, so it still only hits itself once.
The ability doesn't affect this because it would be way less powerful, poison would deal more damage to it due to it getting hurt twice and so on.
Parental Bond allows the Pokémon to attack twice each turn on the same target (even if it fainted), with the second attack being half as strong as the first.
It only has an effect on the attack used by the Pokemon with the ability.
Source: Knowledge and Bulbapedia
Hope I helped.