The king's chapel; i.e. "a sanctuary" (Exodus 25:8; Le 19:30) founded by the king (1 Kings 12:28), not by God. So in truth it had only an earthly sanction, and the prophet of the Lord was out of place there.
The king's court; literally, house of the kingdom. "National temple" (Kuenen); "a royal temple, the state church" (Pusey). Not the political, but the religious, capital, the chief seat of the religion appertaining to the nation.
Amaziah speaks as a thorough Erastian; as if the human authority were everything, and the Lord, of himself, had no claims on the land.