Here's a possibility for Charity in the 1880 US Census:

Name: Charity Collinsworth
Age: 4
Birth Year: abt 1876
Birthplace: Kentucky
Home in 1880: Floyd, Kentucky
Race: White
Gender: Female
Relation to Head of House: Daughter
Marital Status: Single
Father's Name: John Collinsworth
Father's Birthplace: Kentucky
Mother's Name: Nancy A. Collinsworth
Mother's Birthplace: Kentucky

Household Members: Name Age
John Collinsworth
35
Nancy A. Collinsworth
37
George Collinsworth
12
Charity Collinsworth
4
Lila Collinsworth
4
Morg Garrel
18
John Garrel
20
Mary Garrel
17


I think that Collinsworth became shortened to Collins later.

Also, I think that Garrel = Jarrel (relatives of Nancy)

Jackson could be a nickname for John.

All of this is speculation, of course, and needs to be verified with more info....