Elizabeth (Betsy) Wilder was born of a mother, Rhoda Sizemore, who had many children, and by different fathers. Elizabeth Wilder and others are mentioned in a court case as children, and this is when we see her name and existence.
Elizabeth Wilder grew up and had two daughters before marriage. Their father might be a Napier, because in one birth record of a son with Calvin Collins, her name is stated as Elizabeth Napier, and that could indicate a previous relationship prior to marriage with Calvin Collins.
She married in 1850 to a widower, Calvin Collins, who had children with his first wife, and she brought her two daughters to their marriage and home, as evidenced in the 1860 census.
Sources:
The court records of Clay County Kentucky show that at a county court, commenced and held in the courthouse in Manchester on Monday 25 September 1826...
"Ordered that the clerk bind to William Begly [husband of Winnie Sizemore, supposed sister of Rhoda Sizemore] - Nelson Sizemore aged ten years, Dennis Sizemore aged eight years, Betsy Sizemore aged six years, infants of Rhody Sizemore until the males arrive at age of 21 years to learn the art and mystery [sic] of farming, the female until she is 18 to learn the art and mystery of Spinster. . . ordered the clerk to bind to John Bowling-Polly Sizemore aged 9 years, Agnes Sizemore aged 4, until they arrive at age 18 to learn the art and mystery of Spinster." The court records also show that Joseph Wilder apparently filed a motion to have the court order rescinded.
25 September 1826, Clay Co., KY, first three children bound to William Begley.
25 February 1828, Perry County, KY, subpoena to sheriff of Perry Co., KY, to summon William Begley, John Bowling, and Jesse Bowling to have them bring to court Nelson Sizemore, Polly Sizemore, Dempsey Sizemore, Betsy Sizemore, and Agga Sizemore, the children of Rody Sizemore taken from the county of Clay and detained in the possession of the aforesaid persons
William Begley-30, brother in law to Rhoda Sizemore; John Bowling-163, brother in law to Rhoda Sizemore, Jesse Bowling-164, half-brother of John Bowling-163.
Perhaps: William Begley-30 is the father of Rhoda's children who match the DNA of the Begley family. Perhaps Jesse Bowling-164 is the father of the one child of Rhoda who matches the Bowling DNA.
Betsy Sizemore b. 1820, mentioned above, is the d/o Rhoda Sizemore, and was born outside of wedlock. As she grew up, she may have been recognized by her community as Elizabeth Sizemore, her mother's maiden name, or Elizabeth Wilder, using her biological father's surname, as the child of Joseph Wilder-1232.
The fact that her name was given as Elizabeth Napier in her son's 1852 birth record may be explained as an attempt to identify her previous relationship, before Calvin Collins, and perhaps a Napier male was the biological father of her two first children, Mary and Vinie.
Her first two children Mary Wilder b. 1845 and Vinie Wilder b. 1847 were likely born out of wedlock and perhaps their father was a Napier, and thus in her 1852 birth record she was noted as Elizabeth Napier.
https://familysearch.org/ark:/61903/1:1:Q28L-PPXR
Name Calvin Collins Sex Male Spouse's Name Elizabeth Wilder Spouse's Sex Female Event Type Marriage Event Date 18 Dec 1850 Event Place Clay, Kentucky, United States
https://familysearch.org/ark:/61903/1:1:FWN3-VM2
Name Nelson Collins Sex Male Race W Father's Name Calvin Collins Father's Sex Male Mother's Name Elizabeth Nappier Mother's Sex Female Event Type Birth Event Date 12 Nov 1852 Event Place Clay, Kentucky, United States
https://familysearch.org/ark:/61903/1:1:FWN3-RXM
Name Daniel Collins Sex Male Race W Father's Name Calvin Collins Father's Sex Male Mother's Name Elizabeth Seizemore Mother's Sex Female Event Type Birth Event Date 30 Apr 1853 Event Place Clay, Kentucky, United States
https://familysearch.org/ark:/61903/1:1:FWN3-HG8
Name Jane Collins Sex Female Race W Father's Name Calvin Collins Father's Sex Male Mother's Name Elizabeth Wilder Mother's Sex Female Event Type Birth Event Date 15 Apr 1855 Event Place Clay, Kentucky, United States
https://familysearch.org/ark:/61903/1:1:FWN3-8D8
Name Sarah Collins Sex Female Race W Father's Name Calvin Collins Father's Sex Male Mother's Name Eliza Wilder Mother's Sex Female Event Type Birth Event Date 10 Sep 1857 Event Place Clay, Kentucky, United States
https://familysearch.org/ark:/61903/1:1:MZBR-Q58
1860 census, Clay, KY
Calvin Collins 1811 , Elizabeth 1820, Matilda 1838, Polly 1845, Mavil (F) 1847, Viny (Vinie Wilder d/o Elizabeth) 1849, Nelson 1852, Jenny 1855, Sally 0, Mary Wilder (sister of Vinie) 1845.
https://familysearch.org/ark:/61903/1:1:MX7T-149
1870 census, Clay, KY
Calvin, Elizabeth, Viney (Wilder) 1849, Nelson 1852, Ginny 1855, Sally 1858, Malinda 1860, Hannah 1863, Nancy 1864, William 1867, Mary Ann 1870, Thomas 1850
https://familysearch.org/ark:/61903/1:1:MCZ4-17W
1880 census, Leslie, KY
Calvin, Elizabeth, Hannah 1861, Nancy M. 1863, William 1867, Alfred 1872 (this is Alfred L. Wilder, s/o Vinie Wilder and an Unknown Sizemore, as stated on his 1925 death certificate), Henry Wilder 1875 (this is Henry Wilder b. 1876, s/o Vinie Wilder and Wilk Sizemore, as stated on his marriage record to Maggie Bowling. Vinie Wilder is the d/o Elizabeth Napier Sizemore Wilder Collins, w/o Calvin Collins.)
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