The answers to your question are in Eastern Cherokee application #9576, Emeline Smith. The two Alexanders are meant to be the same man. I haven't seen anything with "McGillivray" as a middle name, that seems to be someone's addition to connect him to his grandparents. Emeline wasn't Cherokee, but applied anyway (claiming that grandmother Rachel Durant was Cherokee), so all her genealogy is laid out in the application at Fold3 starting here: https://www.fold3.com/image/221410067
Emeline stated her parents were Alexander Brashears and Emeline Wind (Winn), that his parents were Samuel Brashears and Rachel Durant, and named siblings Sarahanne, Henrietta, Dennis, William, and Louisa.
Quoting from Wells, Dr. Samuel James. Choctaw Mixed Bloods and the Advent of Removal. University of Southern Mississippi. 1987. © Dr. Samuel James Wells, 1987. Used by permission, reproduced at Access Genealogy.
"The Brashears family represents one of the most industrious and influential included in this study. The genealogical thread running through this line can be traced back to the early Scotch trader, Lachlan McGillivray, and his father-in-law, the French trader aptly named Marchand, in Creek country in the mid-eighteenth century (see Chart 4). This family spans the Creek, Chickasaw and Choctaw tribes. Samuel Brashears was an early trader with the Creeks and married Rachael Durant, the mixed-blood daughter of Ben Durant (another trader) and Sophie McGillivray (the mixed-blood daughter of trader Lachlan McGillivray and mixed-blood Sehoy Marchand). 1 His presence was marked by the naming of Brashears Landing on the Alabama River at the spot where he lived."