No official sources, but yeah that appears to be a limitation:
If you are sharing a battle.net account with your kid, you will both not be able to play Plunderstorm at the same time. It is linked to the battle.net account, not the individual WoW Accounts on your battle.net. Was excited to play this with my kid, who I share a battle.net account with, but we are unable to play together.
How to Play Plunderstorm - Installing Modern World of Warcraft - Wowhead
Can’t Play Plunderstorm with my kid - Support / Customer Support - World of Warcraft Forums