There's a story, whose reliability I cannot say, that Shakespeare and a friend went to see a play about a man who marries a nag. The man wraps her in a rug for a week, and bets her mercilessly, feeding her only drops of water and honey. At the end of the play, he unwraps her and she is beautiful and docile. It was very popular and his friend seemed to enjoy the play. He asked Will what he thought and Will said he was horrified. The man said they story was quite popular and asked if Will could do better. will said he could.
So he wrote Taming of the Shrew.
There is a ballad called "A Shrewd and Curst Wife Lapped in Morel's Skin for her Good Behavior." That is probably what you're thinking about (the plot, anyway). There is another play called
The Taming of A Shrew which was at one time considered the immediate source of Shakespeare's play (there's no horse, though); however, I believe the current scholarly consensus is that
A Shrew is a muddled version of
The Shrew. As for the ballad, it's not really close to Shakespeare's play--it's much more brutal. Jan Harold Brunvand (the urban legends guy) argues compellingly that Shakespeare's primary sources for the main plot of
The Shrew was oral tradition. The source of the subplot--the wooing of Kate's sister--is George Gascoigne's play
Supposes, a translation of Ariosto's
I Suppositi.
All Shakespeare's plots were borrowed. Okay, there's no known source for the main plot of
The Tempest, but otherwise, they're all borrowed. And all the other playwrights did the same thing. Sometimes they even updated older plays. Thomas Middleton seems to have edited and added to
Macbeth, and Ben Jonson was hired to add scenes to Thomas Kyd's
The Spanish Tragedy. And then there's the
Ur-Hamlet.
Again, they all did it, and it wasn't considered plagiarism. They took bits and pieces from various sources and reworked them into something new. Take
Two Noble Kinsmen, for example. Shakespeare co-wrote the play with John Fletcher. Its main source is Chaucer's
Knight's Tale. Chaucer's source was Boccaccio's
Teseida. Boccaccio's specific sources are unknown, but he unquestionably had sources. In the Shakespeare/Fletcher play, there is a non-Chaucerian subplot involving a jailer's daughter, who wanders around being mad for a bit. These scenes are
very reminiscent of Ophelia's mad scenes in
Lear. Guess who wrote them? Fletcher. Shakespeare was presumably not bothered by the...homage. Oh, Fletcher also wrote a sequel to
The Shrew called
The Woman's Prize or The Tamer Tamed. It was performed by and possibly written for Shakespeare's company, perhaps when he was still active in it.