From what you have provided, here is what I have found/confirmed.
Kenneth Paul McGaugh md Leigh Anne Evans 1 Aug 1975, both were 16, in Collin Co., TX.Kenneth was born 1 Aug 1959 in Denton Co., TX to father Richard Elmer McGaugh and mother Christine Louella Mace.He was married several times, but I could only find birth records for three children: you, your brother (James Paul), and a half sister (Heidi Lynn b. 9 Dec 1985).Kenneth had at least one sibling, Rebecca Jean McGaugh.
Richard Elmer McGaugh was born in 1928 in Cooke Co., TX to parents William Guy McGaugh and Rosa Lee Nance.The family is enumerated in the 1930 Cooke Co., TX census.There seems to have been another sibling born in November of 1930 (Texas Birth Records), Roy Lee McGaugh.The other children in this family are James W. (b.1924) and Nellie R. (b.1926).
William Guy McGaugh was born in 1900.Rosa was born in 1908.William and Rosa were married abt 1923 (per 1930 census), probably in Cooke or Denton Co., TX.Texas does not have marriage records available to the public for this time frame.Rosa Lee (Nance) McGaugh died 29 Jun 1994 in Denton Co., TX.I found a SSDI record for Guy McGaugh b. 8 Sep 1900, d. Mar 1975.The SS death benefit went to Morton, Cochran Co., TX.I don't know if this is your ancestor, but it seems to fit, so I am offering it up for confirmation. There is also a Texas Death Record for William McGaugh of Cochran Co., TX d. 21 Mar 1975.
William's parents were Elmer and Allie McGaugh.In 1920 they are in Cooke Co., census and in 1910 they are enumerated in the Collin Co., census.I am uncertain how many chidren there were in this family, but I can list William Guy, Amy E., Ray/Roy?, and Eula F.Eula may have died in childhood.
By 1920, Elmer is a widower at the age of 40.That puts his birth at abt 1880.The census says he was born in Texas, father born in TN and mother born in Missouri (It is possible, though, that his mother might have been born in Mississippi).
I have not found Elmer McGaugh and family in 1900, nor did I try to find them in 1880.If you can find them in 1900 you will also find their birth months and years.
I don't know whether we are cousins.We might connect back in TN.My McGaugh line came from Williams Co., TN.They were in Attala Co. and Choctaw Co., MS in 1870, and some family members went to Missouri then to TX, and some went to straight to TX.None of the names in your line are familiar to me, though I do have McGaugh-descended cousins in Denton.Methinks 'tis a coincidence.