Swedish Ancestry - John S Peterson

Dear Wini & Sanna, I could sure use some help. My 2nd Great-Grandfather is John S Peterson. He was born in Sweden in 1831. His wife is Carolina. She was born in Sweden in 1832. They settled in Allamake Co, Iowa about 1866 or 1867.

Some odd things show up in the 1870 US Census for Center Twp, Allamake Co, Iowa.
First John is listed as E. S. Peterson, 31, Carolina, 39, Daughter Alma, 9. Jean, 6 and Charlie my G-Grandfather, 3. His obit says he was born inStockholm, as were Alma and Jean. The 1870 census says Charles was born inIowa. I realize there are mistakes in the census. The 1880 Moline, Rock Island Co, IL census has John S. and Carolina both 49. This fits the cemetery dates. He died in 1889 in Moline, IL and Carolina died in 1881 also in Moline. Other relatives have been to Sweden and said they couldn't find any information so I would appreciate it if you could at least find John and Carolina's birth place and parents names. Thank you for offering to help with Swedish ancestry. I have tried Swedegate.com and can't seem to navigate the site. My lack of knowledge ofthe Swedish language is probably the problem. Thanks again. Sincerely, Steve, Moline, IL