Mike, Congratulations on such an important find!This finally proves that Joseph C. was definitely Joab's son.This finally helps the descendants of Joseph C.'s son, Frank Lane Ainsworth to establish their family line.
I have the son J.P. Ainsworth as James Preston Ainsworth.
As for Evaline Patterson, I noticed that 10 years later, she is shown as 17 years older.If she was really 37 in 1850, then she would be old enough to be the mother of all of the children.It's hard to say which age is correct.Have you found Joab's family in 1870?
A few possible scenarios for the last name Patterson: I have found some women listed with their maiden name on censuses.It is also possible that theirs was a common law marriage.The Patterson children could be Evaline's neice & nephew or the older daughter Susan may have married a Patterson.
The 1870 census could shed more light on these questions.