Daphne was created by Carl Barks, who briefly mentioned her in the 1949 comic Race to the South Seas. When Gladstone defines his family relationship with uncle Scrooge he states: "Scrooge McDuck is my mother's brother's brother-in-law".
In the Duck family tree Barks wrote down in the 1950s for personal use, he gave her the name 'Daphne Duck' and placed her on the tree as Grandma Duck's daughter and Luke the Goose's wife. According to this tree, Gladstone was orphaned when his parents ate too much at a free-lunch picnic, and was then adopted by Goostave Gander and Matilda McDuck, Scrooge's younger sister. 
Daphne's first physical appearance was in 1981, on a portrait on Mark Worden's illustrated version of Barks' Duck family tree. She and her husband first appeared in person in 1993, on a photograph in Gladstone's scrapbook.
In The Invader of Fort Duckburg, chapter 10 of The Life and Times of Scrooge McDuck, a young Daphne can be seen living on her parents' farm. While collecting eggs on the field, she's almost run over by Scrooge McDuck, who is driving his car up the Killmule Hill (currently named Killmotor Hill), but loses control and ended up crashing in Grandma Duck's yard, where Daphne has the luck of getting away just in time. In this comic, she was shown to have an incredible amount of luck, finding a diamond ring in the eggs that she broke during the crash.
Daphne also appeared on Don Rosa's Donald Duck Family Tree, as the wife of Goostave Gander and the mother of Gladstone.
In The Sign of the Triple Distelfink (Uncle Scrooge #310), written and drawn in honor of Gladstone Gander's 50th anniversary, Daphne appeared in Gladsone's flashback. It's revealed that Daphne's birthday is on the same day as Gladstone's birthday, and that Gladstone inherited his luck from his mother.