The Yates family consisted of Kasidy Yates-Sisko and her father, mother and at least two brothers, including the youngest, who was a baseball player for the Pike City Pioneers. It also included Benjamin Sisko and Jake Sisko, by marriage, and her and Benjamin's fetus.
Kasidy's mother would have preferred her and Sisko to be married by a minister, but Admiral William Ross was the next best thing. (DS9: "Penumbra")
Kasidy's father always used to say, "if you're going to do something, do it right". (DS9: "The Sound of Her Voice")
Star Trek literature gives her mother the name Jae Yates (β) and one of her brothers the name Kornelius Yates (β). The baby has the name Rebecca Jae Sisko (β).