The A-plot is that two feuding cousins (unoriginally named McHat and Coyfield) bring their two feuding koalas (also cousins) named Whiskers (McHat) and Sideburn (Coyfield). I say unoriginal because there was a Mickey, Donald, and Goofy short in the House of Mouse era (“Housesitters”) that had them in the middle of the feud and the names of the families then were McHat and Coyfield. Not sure if the writers actually watched House of Mouse, but it is out there.
It’s much more likely that the writers were inspired by the real life Hatfield and McCoy feud, since it is a well known thing in American culture.
No one knows the exact cause of the feud, which is why the Koala’s didn’t know what started the feud in the LPS episode.