Ah, riding a horse along the beach. That's probably the sort of thing that sounds like more fun than it is. The mysterious woman is in front and Theon is behind her. He brags about how good he is at riding horses, and she immediately casts aspersions on his seamanship by asking, "Have these hands ever touched a rope?" He brags some more and feels her up. His hands are all over her breasts and crotch. I mention this because it's going to be important later. And because it tells you something about Theon Greyjoy that he's trying to make out with a woman he just met while they're riding a horse. He tells her he's got a plan for making Lord Greyjoy the new king. And she can come into the castle with him and warm his bed. He brags, "You can tell your grandchildren about this night."
Oh, I like the way the Greyjoys decorate. They have a giant fireplace with a kraken over it. This older gentleman would be Balon Greyjoy, Theon's father. The Greyjoys had some kind of rebellion against the king awhile back, and Ned Stark helped put it down. That's how Theon ended up being raised by the Starks; he was some kind of hostage. Balon asks, "They took a frightened boy. What have they given back?" Theon, instantly reverting to a little boy, answers, "Lord Stark is gone." "And how do you feel about that?" Lord Greyjoy mocks his clothes and the bauble around his neck. He asks, "Did you pay the iron price for it or the gold?" Huh. He has contempt for anyone who pays for stuff. Only weak people participate in commerce, you know. He yanks the jewel off of Theon's cloak and tells him, "I'll not have my son dressed as a whore. My fears have come true. The Starks have made you theirs." Theon boasts about how Robb thinks of him as a brother (which is a great way to convince people you're not really a Stark, right?), and Lord Greyjoy sneers at him. Does Theon remember his brothers, who Ned Stark killed? Theon: "I remember my brothers. And I remember when my father was a king."
Okay, that scene was a lot of fun, but it's time to get to Theon's point. The proposal is that Lord Greyjoy join up with the Starks (which Balon translates as "kill Robb's enemies for him") and he gets to be "King of the Iron Islands."