This looks pretty cool. I've got a couple of suggestions for you, and als a couple of questions, hope that's OK.
Suggestion #1 - The kingdom needs a line of succession. If the king dies, someone should inherit (unless there is a coup.) This leads to:
Suggestion #2 - If a player loses authority, it passes to the next player in the line of succession. So if the king loses 5 authority, the crown prince gains 5 authority. This will also help players catch up with the king!
Suggestion #3, and Questions - You need to be much clearer about what the player goals are. Is it to become king (or queen)? Are there other goals that the players can pursue? How do the rules support the players in stating and reaching their goals?
Hope this helps, and good luck!