She was born Caroline Kramer or Lisette Caroline Kramer (although the only place Lisette is ever used is in the birth index), in Keighley in December 1854, and married as Caroline Krammer, daughter of Louis Krammer, a pork butcher, in Birstall in 1876, to William Broscomb(e). I managed to find what's probably her father in the 1851 census living in Sheffield as Louis Kramer, born in Germany, 1830, occupation journeyman pork butcher. He married a Rose Lair in 1854 as Ludwig Kramer, in Bradford. Rose Lair is Caroline's mother. However, I can't find them on any census as a family, nor can I find Rose anywhere at all. Lair doesn't exist as a surname in Britain and is possibly a spelling error of Lehr, meaning she is also probably German, but when I search for German-born Roses, I don't get much.
One strange lead I found is the Limbach/Limback family. I'll bold the similarities. In 1861, there is a Louis Limbach living in Hull with his wife, with the initials R M. His profession is pork butcher. Two of his children were born in Bradford. There is, however, no Caroline. In 1871 a Limback family is living in Bradford, yet the head's name is George, a shoemaker, but the wife is Rose. A couple of their children were born in Hull, yet there is no Leonard (possibly dead?) and no Caroline. Their daughter, Catherine, was born around the same time as Caroline, give or take, but she was born in Germany, after Caroline's parents were already in England.
Could they be the same people who liked to change their names a lot, including from Louis to George, from Caroline to Catherine and then back to Caroline again, and changing the patriarch's life-long (and ancestral, since his father, too, was a pork butcher) occupation to something completely different in the space of ten years?