"The Twin Sisters", also known as "The Keel Row" or "Smiling Polly" is an English country dance tune in 2/2 time in G Major.
It was published before 1730, according to Raven. The tune is generally known as the Northumbrian favorite The Keel Row.
There are a number of other tunes known as "The Twin Sisters" in America, Canada and Ireland. One is an American variant of "The Boys of Bluehill" (in the Celtic section) and another is a New England variant of "Farewell to Whiskey" (in the Legacies section).
It was printed in Ford's Traditional Music in America (1940), Karpeles & Schofield's A Selection of 100 English Folk Dance Airs (1951) and Raven's English Country Dance Tunes (1984).
It shares some phrases with "Shoes and Stockings". I don't know if there is any real connection.