I've been doing some research on the Joseph Hancock Family from Wilkinson County, GA and believe that we may have a fit.
In Joseph's will, he only identifies 5 sons & 1 daughter, however, the census data shows that he had between 8 & 10 children.
Based on data from the 1820 - 1840 Censuses, I've compiled the following list of children:
S1: b 1794 - 1802 (Probably a brother & not a son)
S2: b 1802 - 1804 (William)
D1: b 1804 - 1810 (Elizabeth m. 19 May 1825 to Lewis Smith)
D2: b 1804 - 1810 (Mary m. 11 Nov 1825 to Jonathan Ridley)
S3: b 1810 - 1815 (James)
S4: b 1810 - 1815 (Edmund)
D3: b 1810 - 1815
D4: b 1810 - 1815 (Elizar)
S5: b 1810 - 1815 (Willis)
S6: b 1815 - 1820 (John)
D5: b 1820 - 1825
If Martha Caroline is one of Joseph's daughters, then she fits in the D5 spot as being born between 1820 & 1825. Since D5 only appears in the 1830 Census, but has disappeared by 1840, it is likely that she either married or died between the age of 15 & 20. Does this match your information?
Regarding my 4great-grandmother, Elizabeth (b 1804), and the Mary (b aft 1804) being part of Joseph's family, I am going based on assumption that since those two Hancock girls married in Wilkinson Co. in the mid 1820s, they might fill two of Joseph's daughter spots. Its still coincidence at this point, but within the boundaries of a single county, coincidence often adds up to something more.
Best Regards & Good Luck!
daniel (at) txmountaineer (dot) com