I am uncertain if I have the right link you are looking for or not. Rinalda Thacker, born in Mississippi in 1858 married Mary F. McDonald, born in the Indian Territory (now Oklahoma) in 1856 and she was said to be a full blood Cherokee or Choctaw Indian. Their oldest son and 2nd child was James M. Thacker, born in Arkansas in in Sept 1882. Per a family history narrative by relative Pauline Decker, James married and he, his wife and infanct died during a flu epidemic when James was 19 years old.
My question is that this James Thacker was the same Thacker as your ancestor? Your ancestor has a different state of birth than the above person, and the above person died early but I am unsure if he left any other descendants or not but given the early death of him, possibly not. It is interesting that your James Thacker has a similar family story on marrying a full blood Cherokee indain lady and that he was married in Hot Springs, Arkansas in the same area that James M. Thacker was from and both James Thackers were born a few years apart . Thre is a picture of James Thacker in this book mentioned above but it is hard to view as something was splashed on the picture of James taken with the rest of his family
In summary, I do not know if the James Thacker you are seeking is the one and same that is my wife's half uncle or not. There are similar things and there is other indications that your ancestor maybe a different person who happened to be in the same town. Perhaps he was a son of one of Rinalda's brothers Oliver or Felix.
I wish you the best of luck and Happy Hunting (for your ancestors that is)!