Billy Gets Grounded is a web series created by Kolin Hildebrand for YouTube in December 2009. It revolves around a main character named Billy, with his parents, Ladonna & Robin, with their two other kids, Molly & Olivia, who ground Billy for doing bad things.
An episode from 2010 “Billy’s Punishment Day” had a deleted scene about Billy’s family and his teacher dancing to the Barney and friends theme song, however, it's not confirmed yet.