Peter: Derek, give me the remote! You are a man of duty!

I think he means, "relieved of duty."

Derek: I don't know why, but when I grow up I just want to own a country.

(First of all, who says that? Only children of Dominte.)

Me: Just a country?
Derek:
Yah, Megan gets to rule the world.

(That's some sibling respect for ya.)

Peter is singing "Piggyback Rider!" (Paperback Writer.)