Below is the 1910 census and death record for Taylor's brother Samuel. And a record that lists the parents of who appears to be their half-brother Charles. Their father's name is listed as Aaron( Allen) Tanner. I see tree's that list Nellie's surname as Rabbit, but no records to support this. Charles' mother is listed as Mary (possibly "Bird or Youngbird").
"United States Census, 1910," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MLQX-4RT : accessed 27 October 2017), Samuel Tanner in household of Charley Tanner, Township 3, Delaware, Oklahoma, United States; citing enumeration district (ED) ED 59, sheet 6, family 48, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 1250; FHL microfilm 1,375,263.
Source info: Original data: Social Security Applications and Claims, 1936-2007. @ Ancestry
||Samuel Neal Tanner
||30 Jun 1887|
||Jay Indian T, Oklahoma
[Jay Indian T|]
||15 Nov 1970|
||1 Oct 1965|
||02 Jan 1976: Name listed as SAMUEL NEAL TANNER; 10 Nov 1977: Name listed as SAM TANNER; 10 Jan 1998: Name listed as SAMUEL N TANNER
Source Citation: The National Archives at Ft Worth; Ft Worth, Texas, USA; Enrollment Cards for the Five Civilized Tribes, 1898-1914; NAI Number: 251747; Record Group Title: Records of the Bureau of Indian Affairs; Record Group Number: 75 @ Ancestry