Mack, if you own a capital ship then the ship is not owned by a faction. So there are no faction protection rights on the ship.
I believe if you enter the territory of a Government faction, Mercenary, Bounty Hunter, Security or Pirate faction, they can arrest you on your own personal capital ship.
If you enter the territory of another type of faction and the faction has authorised another group (Government, Mercenary, Bounty Hunter or Security) to arrest in their territory then this other group could arrest you.
There is no god but Ara... All will walk his path...
The Faithful of Ara
<--- (Warning: music link)