I have been researching the Siegrist, Secrest, Sechrist Family since July 1977 (28 years) and I can answer some of your questions.
Beeson is the 9th child of William and Mary (Beeson) Secrest. Do you have his siblings?
Joseph Cross Secrest married 1) Sally/Sarah Ann Merson, dau of Nathaniel Mershon and Martha Stevens. Sally was born Oct 1786 in Hunterdon Co, NJ; died 24 Oct 1830 in Fleming Co, KY. 2) Ann G. (Moore) Ingraham, widow of John W. Ingraham, who had two children: Joseph who married Ellender Mershon in 1828 and moved to Iowa and Catherine who married Willian Bogges Secrest before 1831. (Ann married the father of her son-in-law) so any descendant of William Boggess Secrest traces their ancestry through both of Joseph Cross Secrest's wives.
I also have a copy of Joseph's will and can tell you that the Emily Faris and Amanda Lewis, who are mentioned in the will, are the children of Joseph and his second wife, Ann. I also have Joseph's obituary which states he and his first wife had six sons and five daughters--actually they had 14 children: 1) William Bogges Secrest (who married Ann's dau)
2) Lou Ann Secrest 3) Melinda Secrest 4) Lydia Secrest 5) Robert M. Secrest 6) Mary Beeson Secrest 7) Charlotte Secrest 8) Joseph Anderson Secrest 9) Sarah Jane Secrest 10) Elizabeth Secrest 11) Nancy Secrest 12) John D. Secrest 13) James Delana Secrest, M.D. 14) Francis Marion Secrest.
Adding the two daughters by 2nd wife: Emily Secrest and Amanda Eleanor Secrest, he had a total of 16 children. Some of his older children died young so they may not have been included in his obituary.
I also want to clarify something else which has created confusion in the past. Joseph's obit states he was born in Virginia on 8 April 1780 which is true, BUT in June 1780, the states of PA and VA negotiated their boundaries and that portion where he was born (Augusta Co, VA) became Westmoreland Co, PA. In 1783 PA made some changes and that portion of Westmoreland Co, became Fayette County. I was born there and I have been to the original farm of Valentine and Susanna Secrest in Lower Tyrone/Perry Twp. (it's on the border) and I have a copy of Valentine's Oath of Allegience which he took on 25 Sept 1772 in Baltimore, MD. (He came to Baltimore from Basel, Switzerland in April 1765.) He remained in MD (Washington Co) until 1778 when he went north into Cumberland Co. PA and in 1779 he claimed land in what is now Fayette County, PA. (see my website for more info.)http://freepages.genealogy.rootsweb.com/~faywest/index.htm
Scroll down to Sechrist.
William Boggess Secrest and Catherine 'Kitty" Ingraham were the parents of at least 22 childlren--some say 23.
I am a descendant of David Sechrist (younger brother of William and uncle of Joseph Cross Secrest and Beeson Secrest.) For some reason (probably Census takers doing) the older sons of Valentine and Susanna became Secrest while the younger sons were Sechrist. The original name when they came from Switzerland was Siegrist.