So it isn't OTR, but there's a small team that put together a podcast modelled on OTR. No spankings, but both of their main series have lots of bratting.
Tales from the Red Panda (
https://decoderringtheatre.com/shows/red-panda-adventures/ ) is about a 1930s style "Man of Mystery" whose sidekick is The Flying Squirrel aka Kit Baxter. She's "secretly" in love with the Red Panda and usually brats around him.
Blackjack Justice (
https://decoderringtheatre.com/shows/black-jack-justice/ ) is a 1950s detective show, where Blackjack has a partner - Trixie Dixon, girl detective. She sometimes brats and almost always banters.