In the usual Greek mythological genealogy, Pandora’s father-in-law was Iapetus.
Iapetus was a Titan and the father of Prometheus and Epimetheus in the genealogy used by Hesiod. Since Epimetheus is Pandora’s husband, Iapetus is identified as her father-in-law by that family relationship. Iapetus’s other well-known sons include Atlas and Menoetius.
This relationship is a genealogical deduction rather than a central event in the Pandora story. Hesiod’s narrative focuses on Zeus, Prometheus, Epimetheus, Pandora, and the troubles released from the container, so Iapetus is not the main character in the episode.
Greek mythological family trees can vary between authors and later traditions. Nevertheless, the standard Hesiodic genealogy places Prometheus and Epimetheus among Iapetus’s sons, making Iapetus the conventional answer. He is sometimes confused with Cronus because both are Titans, but they occupy different generations and family roles.