On the 1930 Atlanta, Cass Co., TX census I found Rebecca Moore [86, TX - should be AL?] living with her grandson, Charles Long [23 TX AL TX] and his wife, Melvina. I then found what I believe to be Charles  on the 1920 Cass Co. census living with Lee Long [46 TX AL AL, medical doctor], his wife, Charlotte [33 LA LA LA] and two other children, Louis  and Hazel Lee . Do you know if Addie was have been deceased by 1920? Is Charlotte a second wife?
However, I also found a Robert Lee Long [bn ca 1873] who died 3/22/1920 and who is buried in Pine Crest Cemetery in Cass Co., TX. So, was he Addie's husband? It's a bit confusing. I find nothing on Addie. I know that in LA the 1920 census was taken in January rather than in the summer as usual. So, if it was taken in January in Texas, then it could be that the Robert Lee Long who died in March at the age of 73 was the same Lee Long who was 46 on the 1920 census.
I still don't find a Rebecca Caldwell, bn in AL ca 1843. I checked 1850, 1860 and 1870. I did find a Rebecca Caldwell [bn ca 1845 in LA] in Rapides Parish on the 1850 census. Her parents and siblings are also shown as being born in LA. Maybe the places of birth are in error.