I always thought it was a bit WTF that Kirk and company so quickly went to an antagonistic mode with Trelene. Obviously this is a highly advanced and unique alien, with tremendous powers and capabilities. I would think "playing along" and learning more about Trelene would have been right in the Enterprise's mission wheelhouse. Of course, we know because of the way the story unfolds later that Kirk's earlier reactions were correct...but at first you'd think that their curiosity and duty as explorers would have tempered their impatience a bit, and they would have viewed this as a "first contact" protocol.
I had the same reactions as I was watching it. On the other hand, it is consistent with 1st season Kirk. He's kind of a dick. "Not a diplomat" as he confesses in "Errand of Mercy."
Indeed, one of the things I didn't like about Pike in SNW in comparison is he's so darned smug and glib. Early Kirk is indecisive, snappish (though he apologizes for it -- three episodes in a row!), and more military commander than diplomat.