If you're a Rival of the Judge, follow these rules:
You may take actions with the Judge's Loyal ships. (Their ships don't add to your control.)
When attacking anyone except the Judge in battle, you may add the Judge's Loyal ships in the battle system to your attacking ships.
When attacking the Judge in battle, Judge's Loyal ships add to their defending pieces, not your attacking ships.
Act: 3
A: The Judge's Flagship is indeed their Loyal ship. You could use their Flagship to build ships, Catapult move, tax using Control Array, etc.