I thought I could help with your post and I went to FamilySearch.org to see what I could find and this is what I found:
1870 Census North Carolina
George Randolph ----------age 54 -----NC
Mary Elizabeth Randolph ------------age 50 NC
Jasper Randolph -------------------age 18 NC
Noah M Randolph -------------------age 16 NC
Thomas C Randolph----------------age 14 NC
Eljah Randolph-------------------------age 11 NC
Cornelius Randolph ------------------age 8 NC
David Randolph------------------------age 4 NC
1860 Census Polk County North Carolina
John Shehane -----------------age 50 NC
Rebecca Shehane-------------------age 45 NC
Rebecca Shehane ----------------age 6 NC
Harriet Shehane -------------------age 4 NC
Richard Shehane ---------------age 3 NC
Hanah Shehane-----------------age 2 NC
Eliza Simmons ----------------------age 10 NC
John Shebastian Shehan b. 1807 Kentucky Died 25 April 1860 Ky
Spouse: Delila Ann Mobley Shehan b. 17 March 1810- Died - 27 Aoril 1881. She was born in Montgomery Co. Md. but died in Nelson County, Ky They are both buried in the Lutheran Church Cemetery in Nelson County, Ky. Her find a grave memorial # 49532169 I hope that is right, I am so sorry but I did this when I was so sleepy and I tried to find something for you to research. I also believe they had 4 children and they are 1. George Grayson Randolph b. 24 Dec. 1880 died 22 Jan 1949 in Yancey Co. NC. His find a grave memorial is 53436746
2. Robert Delbert Randolph --Birth 17 Dec. 1887 Yancey, NC Died 3 Nov 1973 Rutherford, NC Burial Avril Lewis Cemetery, Yancey,NC married Joanna Lewis Randolph His find a grave memorial # 43356623
3. Deemia Randolph b. 16 Sep 1888 Yancey, NC parents are William J. Randolph and Rebekah Shehan
4. Zaney Leona Randolph Jones - b. 18 June 1892 NC Died 28 April 1972 McDowell, NC Burial 30 April 1972 Lewis Cemetery ; I forgot to get her find a grave memorial # But her parents are Jasper and Rebecca Randolph.
Jasper Randolph B. 14 Feb 1852 Died 11 April 1939 Yancey, N. C. Burial in the Randolph (Jasper) Cemetery, Yancey,NC His find a grave Memorial # is 53436773
I am still looking for Rebecca Randolph, it could be that she got remarried which is a possibility, and also a divorce record. so far I am not sure when she did died. but I am hoping I will have an answer soon. Thanks for letting me work on this and if you need help please let me know and I will try to do my best to help. Thanks again. Nancy