Individual Details

Texas marriage records are online at FamilySearch.org and I found this:
E. C. Murphy married L. O. Wylie, 20 Dec 1883, Anderson Co TX

The 1900 Census, Henderson Co:
E. Charlie Murphy, b. Apr 1859, age 41, married 9 years (so definitely a 2nd marriage about 1891)
C. Mollie, wife, b. Dec 1868, 31, has had 5 children - 5 are living
Willie, son, b. Aug. 1891, age 8
Emily, dau, b. Oct 1895, 4
G. Robert, son, b. Feb 1897, 3
Ossie, son, b. Sep 1899, age 9 months
What's odd - there aren't 5 children... Perhaps a child by the first wife was counted but not listed because all of the children listed have been born since Charle married Mollie. You didn't say when Etta Mae was born - could she have been married before 1900? The only daughter is Emily.
It is always possible that if Charlie had children by his first wife, they were living with some of her family and not with him and their stepmother.

I did find another marriage in Henderson Co: E. C. Murphy to Mollie Hodge, 23 Jun 1891 - so there's Charlie 2nd marriage. But I didn't find a marriage for Etta Mae.

If I found Charlie in 1910, he had married again to a Maggie and living in Dallas Co with sons Robert & Ozy and a stepson.

Birth

Apr 1859

Texas

Father	Robert King MURPHY (1834 - 1911)
Mother	Dicey Emily Rogers (1836 - 1871)
Sibling	Elizabeth MURPHY (1853 - )
Sibling	Savilla MURPHY (1855 - )
Sibling	Oza Joshua MURPHY (1857 - )
Sibling	James MURPHY (1863 - )
Sibling	Sarah Martha "Mattie" MURPHY (1865 - 1896)
Sibling	Lawrence Elvin MURPHY (1869 - 1931)