I do not see that you have a family tree on Ancestry. It would be helpful if you let us know what you have already done. Are you descended from one of her sons?
I notice that Nancy is among Blankenships and Hurleys in the 1860 census, so she may well be related to them.
I found the two sons in 1880 living next door to each other in Pike County. I note that both of them left the birthplace of their father blank on the census.
Albert's marriage record to Martha McCoy in 1872 in Logan Co. WV (parent county of Mingo) does not list his parents.
Alford's marriage record to Lizzie Cary in 1876 in Logan, lists his mother as Nancy Allen, but no father is listed.
I believe the the Albert Allen you want died in 1926 in Mingo County, WV. His mother was listed as Mary Blankenship.
I believe that Alford was later known as Richard. He died in Wayne Co. WV in 1938. His father was listed as William Blankenship.
I suggest that you look at the actual death certificates if you have not already done so.
You may be able to confirm that this is the correct Albert and Alford/Richard by getting obits for them. Try the library in Williamson, Mingo County. You can get the exact dates from the death certificates.
My guess (and that is all it is) is that Albert and Alford may be the illegitimate sons of a William Blankenship of Pike County, KY.
If that is correct, then "Allen" may be Nancy's maiden name.
There may well be court records in Pike County regarding support for the two boys. However, it is unlikely you will find these records online. They would have to be searched in person.
If you have not done so already, I would try to find out about Louisa (apparently Nancy's daughter?) in 1860 census.
I note that some family trees give the parents of one or the other of the twins as John Seahorn Allen-Nancy Childress. This seems doubtful as this family was in Illinois and Missouri. Other people give the parents as Jeptha Allen and Nancy Castleman. But this does not seem to be the correct people either.
I would attempt to find every possible record (starting with those online) for the twins and Louisa and put them together in a time line with places and details noted. Keep in mind that Mingo County was not formed until 1895 and that West Virginia was part of Virginia until 1863.
After you are convinced that you have everything you can get from online documents and writing for (cheap) obits for all likely family members, then you will probably have to get access to court records to solve the problem.
Good luck with your search.