Tina, my ancestor, wife of our John Sr. Mitchell was not the Elizabeth Hardwick (who m a John Mitchell) as indicated in several sources. We are actively seeking her identity.
You probably know that your Andrew Mitchell is perhaps part of the Bedford Co., VA Mitchell's,& is not related to my Mitchell's.
You indicate that Robert Lindsay Jr. Hardwick was b 1762. I believe that he was b about 1756 Bedford Co., VA & d May Henry Co.,KY in 1830. There are "Dead Towns" in Henry Co., which helps explains sources saying he lived/died in Grayson Co (Some ref VA, some KY.) I quote from my Notes: "...Franklin was the first town in Henry County. Also Grayson – Hardwicksburg ... Otho" was located in the northeastern section of Henry Co."
Based on sources that I found, he was born next after sister Margaret & younger siblings were b from 1758 to 1773 - all b in Bedford Co., VA.Robert Jr., was the oldest son of Robert Hardwick b 1730 VA, d 1783 Bedford Co., VA, & Elizabeth Jones b bef 1743, d abt 1820 Henry Co., VA. Robt Jr.'s next male sibling John b abt. 1765 was said to have d 5 Feb 1818 Bourbon Co., KY.
Robert Jr.'s first wife Sarah Reynolds & was "b bef 1880" d bef 1800. I listed her that way as I could only prove based on census that she had a male child b 1795-1800 prob. KY.
Robert Jr. m 15 Jan 1810 Scott Co., KY, his second wifeJane Jenny Fauls b bet 1766-1784, d aft. 1830 prob KY. Robert Jr., & Jenny had one female child b bet 1811-1815 Henry Co.,KY -easily proven by census.
As to Dorcas, I do not have children's names identified b to Robt Jr. & Sarah. I suspect as typical of those times that there would be others besides your Dorcas b 3 Jan 1786.
Here are some of my Notes that may be of interest to you: " Robert Jr.'s next neighbors in 1820 were three Mitchell families that are unrelated ---all on page 22 of 29: Tho W Mitchell, 1820 census: West Port, Henry, Kentucky, August 7, 1820: Males - 26 thru 44: 1; Females - Under 10: 2; 26 thru 44: 1. Geo K Mitchell, 1820 census: West Port, Henry, Kentucky, August 7, 1820, Males - Under 10: 3; 10 thru 15: 2; 45 and over: 1; Females - Under 10: 1; 45 and over : 1. NOT INDEXED BUT film says: Edward Mitchell, 1820 census West Port, Henry Kentucky, August 7,1820: Males 45 and over : 1, Females, 10 thru 15: 1; 45 and over: 1. (Compiler: perhaps sons of John Mitchell, died 1770, Sussex Co., VA???)