Carolyn's 2nd-great-grandparents have four children on record: Stina Maria, Nils Petter, Carl Johan (her great-grandfather AKA CJA Peterson), and Cajsa Lena.
15 May 1868 Nils Petter emigrated destination Nordamerika traveling alone.
2 Apr 1869 Carl Johan emigrated destination Galva
9 Jun 1871 Stina Nilsdotter emigrated destination Chicago with Clara age 11. This is not Carolyn's 2nd-great-grandmother as I was speculating.
Researching the family, I found lots of new information. I am using the surname Pehrsson since that is on their baptism records
Daughters Stina Maria and Cajsa Lena both married and died in Kristdala.
I found Stina Maria in the Hultgren-Gustafson Family Tree by Ingvar Hultgren. It did not include her three siblings. It includes seven more generations to your 9th-great-grandfather.
I found Cajsa Lena in the Ålstam släktträd by Anders Ålstam of Gunnebo, Kalmar, Sverige. It did not include her three siblings but identified Petter Nilsson's parents.I did not include them since there were no source citations.
I think Nils Petter died in Chicago in 1897, but I cannot prove it without ordering the death certificate,