I may have answered some of your questions. On the 1870 Davis Co., Texas census I found that Dudley and Anna's two children were living with Anna's parents, Lewis E. Watson and Elizabeth Watson. The census reads:
Davis Co., Linden Post Office
Lewis E. Watson 45 AL
Almedia D. 15 TX
John S.D. Moore 3 TX
Nettie A. 10 months LA
A few houses down, Dudley Moore, 25, bn AL, deputy sheriff, was listed.
In 1860 I found the Watson family. The census reads:
Cass Co., Courtland Post Office
L.E. Watson 37 AL
E. 39 TN
A.E. 14 TN [This would be Anna E.]
R.J. [or I.] 12 TN
S. E. 7 TX
A. J. [or I.] 5 TX
A. B. [or D.] 1 TX
All the children were girls. Listed near this family were the following:
L. Watson 69 GA
P. 71 SC
Next door was:
E.S. Watson 32 AL
S.W. 25 TN
It is likely that the first couple was the parents of Lewis Watson and E.S. was likely his brother.
On the 1880 census, I found the following:
Dudley G. Moore 35 AL
Rebecca A. 35 AL
Nettie A. 10 LA
Carra E. 4 TX
Mary A. 1 TX
The little boy, John, may have died since he is not with his father in 1880. Or, he may have stayed with his mother's people.
I found the Moore family in 1860 in Upshur Co., Point Pleasant P.O. in Texas. The father is listed as Dudley and the mother is Amanda. Perhaps you have found this census. It appears that family may have moved to Texas between 1854 and 1856.
I did not find anything on Rebecca's parents. Since she married in 1874, the family may not have left Alabama until after 1870. I don't find them in LA or TX. I also found nothing on Dr. Long.
I hope this helps with your research.