Emmet Otter's Jugband Christmas (Children's book, 1969)

Adapted from Wikipedia:

The story tells of Emmet Otter and his Ma, a widow. They scrape by on the small amount of money she gets from doing laundry and Emmet earns from doing odd jobs around their home town of Frogtown Hollow. Both are often cheated, notably by Old Lady Possum and Gretchen Fox (the wife of Mayor Harrison Fox). As Christmas approaches, they hear of a talent contest in the nearby town of Waterville, and separately decide to enter to buy nice presents for each other—a nice guitar for Emmet, and a piano for Ma. However, in a twist on The Gift of the Magi, they must sacrifice each other's livelihood for the talent contest. Ma hocks Emmet's tools for dress fabric, while Emmet turns Ma's washtub into a washtub bass for a jug band. Emmet and Ma each do an excellent job (despite Emmet's jug band having to frantically change songs after another contestant performs their song, Bar-b-que), only to be defeated at the last minute by a rock-and-roll band called The Riverbottom Nightmare Band (most likely due to the nasty Gretchen Fox on the judging committee), which comprises a hoodlum gang from the fairly distant town of River Bottom made up of Chuck Stoat, Fred Lizard, Howard Snake, "Pop-Eyed" Catfish, and Stanley Weasel. But maybe Emmet and Ma are lucky yet...

The book was adapted into a 1977 one-hour TV special by Jim Henson: