I'm guessing your mention of The Big Valley is the episode titled "The Brawlers." Very early in the show--before the opening credits--Audra, the young adult daughter in the family played by Linda Evans, gets into a heated argument with settlers she thinks are trying to steal her family's land.
Though she does truly think they are trespassing or worse, she gets quite physical as the argument progresses, repeatedly trying to knock the group's leader down as she rides past him on her horse. At last, he reaches up, yanks her off the horse and holding her bent over with her feet just off the ground
(sort of an over the knee position without her actually being over his knee)gives her 9 or 10 good hard spanks to the seat of her jeans.
Evans does a good job thrashing around and crying out.
As this happens, the group of settlers watches from a short distance away. After the 9 or 10 spanks the camera moves from the spanking to this group and they are shown cheering and laughing as the audience hears the last couple of spanks land.
A great scene. There's also some followup dialogue elsewhere in the episode commenting on the spanking.