First quick look shows two records under "Tutor", four under "Tudor", one under "Tudar", and some other data under "Tudor" related to children births & christenings.
1880 Census, Upper Young Cane, Union, Georgia
Robert Tutor (60); Nancy A Tutor (57); Margarett Tutor (19); Sarah Tutor (17); Jessee (14, son) [all these children born in Tennessee] plus a granddaughter.
Both Robert's parents were born in Virginia.
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M8P3-C92 : 11 August 2017), Robert Tutor, Upper Young Cane, Union, Georgia, United States; citing enumeration district ED 177, sheet 113A, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0169; FHL microfilm 1,254,169.
Second is a death record for Robert Sidney Tutor or Tudor, son of Robert G Tutor or Tudor and Nancy Butler (not Blalock), born in Brunswick Co, VA - who died 30 Nov 1947 aged 74:
"North Carolina Deaths, 1931-1994," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FP6K-LKQ : 18 July 2017), Robert G. Tutor in entry for Robert Sidney Tutor or Tudor, 30 Nov 1947; citing Littleton, Halifax, North Carolina, 29245, State Department of Archives and History, Raleigh; FHL microfilm 1,926,629.
From the 1900 US Census, we can work out Angeline's date of birth as approx. 1845, and see that Robert Tudor lived at least until 81, and Nancy Tudor until 77.
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MSCX-B6L : accessed 21 January 2018), Robert Tudor in household of Phillip Malone, Civil District 18 Athens town (part), McMinn, Tennessee, United States; citing enumeration district (ED) 89, sheet 15B, family 303, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,241,585.
We have Brunswick VA birth records for Robert S Tudor (10 Apr 1874) and Banister Tudor (Feb 1860) both as sons of Robert G Tudor and Nancy Tudor.
An 1850 Census Record shows Robert Tudar 30 and Nancy Tudar 27 with three children Elly Ann 7, Rebecca C 5 and Mary C 3.
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MCD2-916 : 12 April 2016), Robert Tudar, Jefferson county, Jefferson, Tennessee, United States; citing family 732, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
Other research shows that Nancy Blalock (married name) was born 1790 and died 16 Dec 1856. She had several children that kept the name "Blalock", but her daughter Nancy chose to use the name "Black" instead.
Robert G Tudor appears to have joined the 12th Virginia Infantry in the Confederate Army in 1862 - but I cannot currently access the full record.
So adding together the above results, plus other data not referenced:
(1) The correct family name would seem to be TUDOR, which may originate from English ancestors. "Tutor" and "Tudar" seem to be misspellings or phonetic mistakes transcribed in some documents. The correct father name seems to be "Robert G Tudor".
(2) Nancy Blalock was actually the name of the wife's mother, and I have yet to find any records ascribing it to the daughter born in 1823 (Robert's wife). There is one instance of "Nancy Butler" as his wife - probably an error - but otherwise in most records it seems to be "Nancy Black", or her married name "Nancy Tudor" or corruption thereof.
(3) I have yet to find any records for two daughters you advised Mary Ann and Katie. So far I have located evidence of 14 children as follows: Elly Ann (b.1843); Rebecca C (b.1845); Angeline (b.1845); Mary C (b.1848); William (b.1850); John (b.1852); Nancy Angeline (1854-1928); Joseph N (1856-1940); Robert W (b.1859); Bannister (b.Feb 1860); Margarett (b.1861 Tennessee); Sarah (b.1864 Tennessee); Jessee (son b.1867 Tennessee); Robert Sidney (b.10 Apr 1874 Meherin, Brunswick Co, Virginia-1947). The family appears to be inter-racial. It looks like Angeline and Mary C are twins.
(4) The family moved around between NC, VA, GA and TN.
Anyhow, I hope that provides some additional lines for you to follow.