Who were the true children of Rev. John Lawler and who were the 12 children he only raised?

Question

Rev. John Lawler was born 1818 in TN and died 1899 in Illinois. When he was 14 his family moved to Fayette County IL. His wife Jane Matthews Mathias born 1828 in KY also came to IL with her family. John beame a Primitive Baptist pastor when he was 35. According to a family story John and Jane raised several children who were not their own. They had 12 children of their own, took in 5 of his brother's orphaned children and 5 grandchildren. They also raised 2 unrelated children. In all the census, I have found 17 Lawler children - all supposed with the last name of Lawler and all supposedly his children. I would like to know who were the children in his direct line and who the other children were.

Answer 1

https://familysearch.org/search/record/results?count=20&query=%2Bfather_givenname%3Ajohn~%20%2Bfather_surname%3Alawler~%20%2Bmother_givenname%3Ajean~&birth_place2=10%2CIllinois%2CFayette

 

these three (Sarah, Helen and Mary Catherine) are definitely theirs, I guess.  The span of birth years here is 1850 through 1871.  The children in the 1880 federal census are probably their biological children but that is the first federal census which gives relationships.