Cont.: 
The not-so-pretty daughter is nicknamed "Tatterhood" because she decides to wear a tattered looking hood/cloak all the time, but she's actually kind of a kick-butt character and proves to be pretty smart as well as strong. One Christmas, a bunch of trolls/witches are causing havoc in the castle like they do every year, and Tatterhood decides to drive them out so they can all have some peace for once. She tells her parents to keep her sister safe while she does so, but returns after driving them out to find that someone goofed up and let the witches/trolls replace her sisters head with a calf's head. After scolding the people responsible, she takes a ship and sails to the island where the witches/trolls live and fights them to get her sister back to normal. After that, the two girls sail off on their own and explore the world until they eventually arrive at a kingdom and the people get curious about what's going on with the ship. Upon investigation, Tatterhood is charging around the deck on her goat, but refuses to let anyone see her sister unless the king shows up. When the king shows up, Tatterhood introduces him to her sister and the two decide to get married. 

...Except, the sister says that she won't marry him unless Tatterhood gets a husband as well...