I found her as daughter of Christian August II. of Schleswig-Holstein-Sonderburg-Augustenburg (1798-1869) and Countess Louise Sophie of Danneskiold-Samsøe. Due to his marriage with an unequal woman he lost his claim to the danish throne. His pro-german political position and his participation on the german side during the First Schleswig War led to his retreat from Denmark. He lived with his family in Primkenau in Silesia.
Karoline Amelie was born in 1826 as third of seven children. Through her brother Frederik she was the aunt of Empress Auguste Victoria. Her brother Christian married Princess Helena, daughter of Queen Victoria. (Informations from wiki, sorry.)

With the flaws in her pedigree - an aspect that also led to discussions regarding the marriage of her niece with Prince Wilhelm of Prussia - and the limited financial resources of the family it might be difficult to get her a husband, perhaps a reason she stayed unmarried. She died in 1901 in Cairo, according to additional informations about a picture in the Schleswig-Holstein State Library.
http://www.museen-nord.de/Objekt/DE-MUS-076111/lido/P4-L-28