The Bad Seed was a play before it was a movie. At the end of the play, when the actors and actresses were taking their bows, the actress playing the mother would flop the Bad Seed over her lap and "spank" her. My guess is that it was mostly acting, but there might have been nights when the kids were off her cues and the spanks were hard enough to be felt. Most of the original cast were hired to do the movie - including the people playing the mother and daughter.
The movie was one of the first ones in the 50s where the "bad people" came out ahead - which wasn't allowed under the Production Code. That means they had to change the ending, having God himself strike down the Bad Seed, but the producers were concerned that it wouldn't be enough. To remind people that "it's just a movie" they actually had a current call like sequence tacked on to the end of the movie, where the actors entered and were credited for their work. With that happening they included the "And as for you..." scene at the end. It was something that had happened hundreds of times during the play, and one last time during the movie.
While you can see the smacks land, my guess is that they where mostly playful acting - especially since the girl is smiling as they land. Anyway, the entire scene (that starts with "the end" flashing) can be seen at:
But back in the 60s (and earlier) it's possible that many movie spankings were real - and some of the actors biographers say they were. Then there were things like the handing caning scene in Kes that the young actors were told would be faked, but were real (the actors "were paid an additional 50 pence") but various "School Days" shows from the same period had the kids wearing specially padded trousers so they would barely feel the cane land - it coming down more as a tap than a whack.
But that was then. Occasionally you see "spanking" in a modern movie, but they are practically all fake. For example,
Divine Secrets of the Ya-Ya Sisterhood has a scene where a woman is chasing her kids with a "belt" and if you listen to the commentary you will learn that the "belt" was a specially treated piece of velvet that the kids barely felt (some of them missed cues because they didn't notice the "belt" landing). Other movies include so much padding that the actor wouldn't feel a prison caning. Sometimes there is actually impact that the actor feels, but that's up to the actor involved - and only when it the actor is an adult who can make that decision.