In 1900 and 1910, they must have lived in El Paso Co., TX because Culberson County was created on March 10, 1911 from El Paso County.
I'd contact the El Paso County Genealogical Society to see if they have anything about your family.
Married: 20 May 1904, El Paso Co., TX
Miss Alcadia Martinez
Source: TX County Marriage Index 1837-1977
Nicholas Martinez Benavidez
Born: 14 May 1928, Culberson Co., TX
Father: Gil Benavidez
Mother: Alcardia Martinez
Source: TX Birth Index 1903-1997
Born: 4 May 1934, Culberson Co., TX
Father: Gil Benavides
Mother: Acadia Martinez
Source: same as above
Isidora G. Rodriquez
Died: 29 Oct 1947, Culberson Co. TX
Source: TX Death Index 1903-2000
I'd contact the Permian Historical Society, http://permianhistoricalsociety.org/
and ask if they have Isidora's obit or other info about your family.
The University of Texas-El Paso, www.tsl.texas.gov/arc/local/culberson.html
has deaths 1911-1972 and marriages 1911-1973 for Culberson County on microfilm. Your local, public library can request the microfilm via inter-library transfer.