Here is what I have found about Ernest Murphy.
The 1920, 1930, and 1940 census shows him in Livingston, Alabama, as you said. He is a college teacher, as you said.
Precinct 7 Livingston, Livingston Town, Sumter, Alabama
Ernest J Murphy 42 born about 1878 in Kentucky
Callie S Murphy 33 b abut 1887 in Alabama
Ernesttine Murphy 7 daughter b Alabama [b 1913]
Jasmie C Murphy 3 daugher b Alabama
Livingston, Sumter, Alabama
Ernest J. Murphy 52, married, boarder, b about 1878 in Kentucky
Livingston, Election Precinct 7, Sumter, Alabama
in the household of J. L. Parker….
E. J. Murphy 62, widowed, lodger, b abt 1878 in Kentucky, teacher, college
E. J. Residence in 1935: Same House (a question on the 1940 census)
Edward's wife Callie is an inmate at a hospital in Tuscaloosa, Tuscaloosa, Alabama in 1930 and 1940. I do not know where the girls are in these years.
Someone has listed Ernest and family on an Ancestry.com family tree:
Ernest James Murphy was born in Pembroke, Christian County, Kentucky on 13 Oct 1877 to Edward J. Murphey and Annie Hurd and died 20 April 1970 in North Pickens, Alabama.
He married Callie McKee Stakely (born 06 Dec 1886 in Alabama; died 28 Mar 1974 in Greensboro, Alabama).
Ernest and Callie’s children - 2 daughters:
*1) Callie Ernestine Murphy (called Ernestine) born 04 February 1913 at Union Springs, Bullock, Alabama and died 04 April 2009 in Tyler, Smith, Texas.
Ernestine married Harvey Eugene Brasher (1907-1972). In 1952 this couple lived in Tokum, Texas (per Harvey’s father’s obit).Three children (see her obit below).
*2) Jaimie Carolyn Murphey (1916 - 1983) married Emerson Ward Blakney 12 April 1942 in Tuscaloosa, Alabama. Three children (see more about them on the links):
*** Carol Goulding Blakney (1944-1996)
MARSHALL [Texas] - Services for Ernestine Brasher, 96, of Tyler, formerly of Marshall, will be 4 p.m. Wednesday, April 8, 2009, in Colonial Gardens Cemetery, with Chaplin Elwood Stetson officiating. Arrangements are by Sullivan-Heaster Funeral Home. Mrs. Brasher was born February 4, 1913, in Union Springs, Alabama, and died April 4, 2009, in Tyler. Survivors include her children, William Ernest Brasher, Nettie Jean Farrow and Carolyn Anne Kuykendall. Buried Colonial Gardens, Marshall, Harrison, Texas [as is her husband Harvey].
Jaimie Family Webpage
This webpage (link above) refers to Jaimie Carolyn Murphy (1916 - 1983). If you click on the names of her children, you will see much more information, including descendants you could get in touch with.
Click kon the link below to find a photo of a man holding a little girl; presumably this is Ernest J. Murphy holding Jaimie:
This website might help you contact this family and might be able to lead you to other relatives. The maker of the website encourages people to contact him. He has posted his email online: captjohnblakeney @ earthlink.net (all run together; no spaces)
I believe Jaimie's son William died in Reform, Pickens, Alabama after the web page was made? He and his parents are buried in Reform.
A Memorial on Find-a-Grave website to Jamie Murphy Blakney: