I am not afraid to admit my mistakes. My book apparently has two rather large error, but tying the lines together as I did was not arbitrary or wishful thinking. There were other pieces of evidence that helped me draw my conclusions:
1. DNA evidence appears to be conclusive that Thomas Carter of Amelia c.1780 - 1828 is descended from Thomas Carter of Goochland c.1680 - 1738. But Raleigh Carter of Amelia/Nottoway did indeed have a son named Thomas, named in his will in Nottoway in 1820. I searched every county within three counties in every direction of Nottoway for an unclaimed Thomas Carter that perhaps had offspring with some of the names of the Thomas Carter of Lancaster clan, but failed to find one. I connected Thomas, son of Raleigh, to Thomas of Amelia through his wife, Catherine Muse. Thomas Carter and Catherine Muse, daughter of Hopkins Muse, had a son, Henry W. Carter, who married Martha America Carter, daughter of Jesse Carter (of the Thomas Carter of Lancaser family) and Sally Wrenn Muse. This made Catherine Muse and Sally Wrenn Muse second cousins. It was certainly not uncommon at this time in our country's history for families to intermarry multiple times. It was from this that I drew my conclusion.
2. My other mistake goes to the very nature of the subject of my book: tracing my Carter family back to immigration. John Carter of Amelia is my last positively identified ancestor, 1775 - 1852. All information from him to the present day is lock solid. I had attached John to Waddill Carter, who in 1782, named his young son John in his will. The information going backward from Waddill to Theodor in Cirencester, Gloucestershire, England also appears very conclusive. However DNA evidence does not support a descent from Giles Carter of Henrico. I made my conclusion based on the unique middle name of one of John's sons, Beverly Atwood Carter. The Atwoods resided in Prince Edward County. I was able to find documented evidence of interactions between Waddill Carter and William Atwood, son of James Atwood (died 1771 in PEC). Far more frequent were the interactions between the family of Waddill's wife, Mildred Wade and the Atwoods.
While the source of the Atwood name in my family is indeed from this group of Atwoods, this was not the connection. John had three children: William Ryland Carter (1809 - 1886), Beverly Atwood Carter (1813 - 1862), and Mary Elizabeth Carter (1820 - after 1880). John marries Oney Pollard in Amelia in 1821, but the birthdates of his children indicate there must have been a first wife, whom I had never been able to locate. I have done some extensive research since receiving my DNA results, and I have come to learn that John's first wife was a daughter of James Vaughan and Lucy Jeter of Amelia. James' Vaughan's aunt was Mary Vaughan, who first married John Turner, and then, as a widow in 1759, remarried to James Atwood of PEC. Lucy Jeter was the aunt of Samuel Beverly Jeter born 1786 and Ryland Jeter, both sons of Samuel Jeter. Her nephew Sovereign Jeter also had a son named Beverly Ryland Jeter, born 1817. The source of the Beverly and Ryland names in the Jeter family come through Lucy's uncle, Samuel Jeter, who married Mary Dudley, whose mother Ursula Beverly is the source of the Beverly name. A Mary Dudley also married Joseph Ryland in Essex Co., VA in 1751. The true source of these unusual names has finally been recognized. I need to do further research to discover the father of John Carter.
So there it is. I published two large errors, but not out of deception or a rush to publications or a lack of research. I had support for my conclusions, but I recognize the DNA evidence, and it has at least set me on the right path now. I will probably publish a newer edition in the future, correcting my mistakes, but not until I have more data that also jives with the DNA findings.