Have you checked the following site?
http://freepages.genealogy.rootsweb.ancestry.com/~wilsweik/index.htm.
There is some Peuker info there. I have found some mistakes in my Handkes, but it is a place to start.
This site has from a ship's passenger list: Johann Gottlob Peuker 1828-1876 married to Caroline Geppert 1818-1901. Children Julius Peuker, 1857-1888; Anne Peuker 1859-1880, Emma Peuker 1862-1898; William Klinnert 1844-1888; Fredrick Klinnert 1853-1918. Ship "Hammonia" arrived 1872.
Caroline Rose Peuker Klinnert or Klinnert Peuker [I've seen it both ways] is also a daughter, she arrived on the ship "Germania" in 1869 with her husband William Handke and son Karl Traugott (Charles T.).
There's quite a gap between William Klinnert's birth in 1844 and Frederick's in 1853, and Caroline Rose's in 1854. Makes me wonder if there were other children.
Some researchers have Caroline Geppert married first to a Klinnert. According to the children listed above that sounds right. They also have her daughter Caroline first married to August Carl Klinnert. And that William Handke adopted her son Charles. It's possible, but Charles was born April 1868 and by June 1869, Caroline Rose and William were married and on their way to America. Charles Handke's obit doesn't mention a father named Klinnert. According to his obit his father was William Handke. Needs more research.
I haven't really done any research on the Peuker line yet. Caroline who married William Handke is the only Peuker that I know of in the Handke family, and my line is through William's brother Gottlieb. I've just this month started researching the other family lines that came from Germany in hopes of learning more about my Handkes.
I understand that there were about 60 families that came from that small area of Germany to Atchison and Doniphan Counties, Kansas. It wouldn't surprise me if a lot of them weren't connected by marriage long before they arrived here.
Do you have much info on Caroline Rose Peuker Handke's father William and his brothers Gottlieb and Gottfried? None of us can get past these three brothers. We sure would like to know their parent's names.
Janet