Hi Patricia, Here's a little help. First, Findagrave.com shows Mattie buried in the Heards Prairie-Petteway Cemetery in Bremond (Robertson Co.). She's the only Vawters listed there, but there's no way to know if a complete cemetery enumeration has been done.
Family Search has Texas Death certificates to 1976.
Joe's death cert info: Name: Joe Welsey Vawters Death Date: 27 Apr 1962 Death Place: Tom Green, Texas Gender: Male Race: White Death Age: 62 years Estimated Birth Date: Birth Date: 15 Oct 1899 Birthplace: Texas Marital Status: Married Spouse's Name: Father's Name: Sam Vawters Father's Birthplace: Mother's Name: Ola Griffith Mother's Birthplace: Occupation: Cattle Trader Place of Residence: Groesbeck, Limmestone, Texas Cemetery: Groesbeck Cemetery Burial Place: Groesbeck, Texas Burial Date: 28 Apr 1962
Here's Sam's death cert info Name: Samuel A. Vawters Death Date: 25 Dec 1951 Death Place: Rosebud, Falls, Texas Gender: Male Race: White Death Age: 85 years 12 months 25 days Estimated Birth Date: Birth Date: 15 Dec 1866 Birthplace: Mississippi Marital Status: Married Spouse's Name: Father's Name: John Vawters Father's Birthplace: Mississippi Mother's Name: Mother's Birthplace: Occupation: Farmer Place of Residence: Rosebud, Falls, Texas Cemetery: Kosse Burial Place: Kosse, Texas Burial Date: 27 Dec 1951
His death certificate says he's married and the informant was Mrs. Joe Vawters.
Here's Ida's info: Name: Ida Vowters Death Date: 19 Apr 1940 Death Place: Marlin, Falls, Texas Gender: Female Race: white Death Age: 70 years 7 months 4 days Estimated Birth Date: Birth Date: 15 Sep 1870 Birthplace: Kentucky Marital Status: Married Spouse's Name: L.A. Vowter Father's Name: Don'T Know Father's Birthplace: Don'T Know Mother's Name: Don'T Know Mother's Birthplace: Don'T Know Occupation: Housewife Place of Residence: Kosse, Texas Cemetery: Powers Chappel Burial Place: Burial Date: 19 Apr 1940
Informant is William Vawters.
Not sure who the next one is, but is probably connected somehow. Name: Delphia Vawters Death Date: 20 Apr 1954 Death Place: Kosse Rural 1, Limestone, Texas Gender: Female Race: White Death Age: 75 years 5 months 12 days Estimated Birth Date: Birth Date: 08 Nov 1878 Birthplace: Texas Marital Status: Widowed Spouse's Name: Father's Name: William Shelton Father's Birthplace: Texas Mother's Name: Elizabeth Jones Mother's Birthplace: Texas Occupation: Housewife Place of Residence: Kosse Rural 1, Limestone, Texas Cemetery: Eutaw Burial Place: Kosse, Texas Burial Date: 21 Apr 1954
Ora Vawters is the informant.
Since that database only goes to 1976, it's possible many of the children were still alive.
In the Texas Death Index to 2000, (still on Family Search), there are quite a few Vawters. Without parents names in the database, it's hard to narrow it down. Here are a few of the interesting.probable ones:William, d. 1986 in Brazoria Co., a Julius d. 1994 in Robertson,Lillie d. 1982 in Falls Co.,
Finally I checked the Texas USGenWeb. There's a Mattie Vawters married to a Willie Sapp who has a baby in Falls Co. in 1933. Connected?
There's also a J.W. Vawters married to Lillie Sapp (see above) who have a baby in Bell Co. in 1932. Another Sapp!
Well, my head is about to start spinning. :) You may have already seen most of this. If not, I hope it helps. Please let me know if you have questions or need the url for anything.