"The King Who Wished to Marry His Daughter" is a Scottish fairy tale collected by John Francis Campbell in Popular Tales of the West Highlands, listing his informant as Ann Darroch from Islay.
It is Aarne-Thompson type 510B, unnatural love. Others of this type include Cap O' Rushes, Catskin, Little Cat Skin, Allerleirauh, Donkeyskin, The She-Bear, Tattercoats, Mossycoat, The Princess That Wore A Rabbit-Skin Dress, and The Bear.
Synopsis
A king lost his wife a long time ago, and declared he would not marry anyone who did not fit her clothes. One day, their daughter tried on her dress and found it fit. Her father declared he would marry her. At her foster-mother's advice, she put him off with demands for clothing: a dress of swan's down, a dress of moorland canach, a silk dress that stood on the ground with gold and silver, a gold shoe and a silver shoe, and a chest that could lock inside and out, and travel over land and sea. When she got the chest, she put her clothing in it and got in herself, and asked her father to put it to sea, so she could see how well it worked. It carried her off to another shore.
There, a herder-boy would have broken it open, but she got him to get his father instead. She stayed with his father for a time, and went into service at the king's house, in the kitchen. She refused to go to the sermon because she had bread to bake, and sneaked off to go dressed in the swan-down dress and the king's son fell in love with her. She went again, in the moorland canach dress, and then in that of gold and silver, with the shoes, but the third time, the king's son had set a guard, and she escaped, but leaving a shoe behind.
When the king's son tried it on women, a bird sang that it was not that one but the kitchen maid. Every woman failed, and he fell ill. His mother went to the kitchen to talk, and the princess asked to try it. She persuaded her son, and it fit. They married and lived happily ever after.