William is Jim's son , no dought, the Hugh you mension is also Jim's son and brother to Wm how md Hammer.
the confusion is caused by the Hugh's - this Carothers line is the only one that uses the name- and is used by the five sons of Robert aka Ol Robin.Kicking around Orange county an the best way to state it is the original Orange County which includes Cabarruss,Mecklinburg and Gaston Counties , Hugh Sr. was the 1st one in 1757 and held lands in Orange Co., and the other 3 mensioned above.There is No confusion as to this Hugh and this Hugh settled in Madison Co,Ala, His cousin Hugh in the area is Robert & Marg Gillespie Carothers grandson , he is the James, this James if 1st cousin to your James in Jessamine Co.,Ky. This Hugh md the daughters of Andrew Carothers , Not Hugh Jr son of Hugh Sr. your GGGGF . and their is two more , Hugh Hill Carothersthis one was born to James & Agnes Neely Carothers ,brother to my ancestor, and one more who remained in Cumberland Co,Pa born shortly before the Hugh you in question of. and he is belongs the 1st cousin of Hugh Sr and his siblings, he is also the nephew of Margaret Gillespie Carothers wife sister in law to Hugh Sr. and to Col.Thomas Gillespie of Rowan Co,NC. (my ancestor).
This is the family loop and who the Hugh's are in the records.At this time I donot agree Nancy Scott wife of James Carothers - Mother is a Thornton, It would be nice if this were a fact- the fact we do know is Nancy is sister to my Margaret who md Robert , This Scott saga we all are still working on. Just before my open heart work Ken and Charle Scott which are Scott/Carothers had proved Old one armed John, Abe and couple of other Scott's we are concerned with are in related - this proven by DNA.
Have you found anything supporting the NC Scott boys married the Thornton's other then one arm John ?
Take care Cuz