Thank you for your helpful and informative posting.
Here are a few differences.
The Trail of Tears happened in 1838. Mary Adams, wife of Thomas Alford, was born c1835 in GA. In 1840, her parents were in Harris Go GA and Mary married there in 1850, so her parents did not go on the Trail of Tears. Mary's parents did not even go to AR later because her father John Adams was still in Harris Co GA in 1860 (age 66 NC). (He seems to be omitted from the 1850 census.)
The 1860 Harris Co GA census of the Thomas Alford family shows the following children: AJ 9, Amanda 8, Josephine 5, Fanny [Phada?] 4, Ida 3, Infant (m) 4/12.
In 1870, the Alford children were: Andrew 19, Amanda 17, Josephine 14, Eida [Phada?] 12, Thomas 9, Ida 8, Christanna 7, Juliet 4, Billie (m) 5/12. The 1860 daughter Ida should be 13 in 1870 but is not in the household, but there is a new daughter Ida.The Ida born c1857 must have died 1860-1862 and there was a second daughter named Ida (born c1862). So, it seems that Thomas and Mary had 13 children rather than 12.