Debi, I do not think that William Clark Atkins was a sibling to Madison and Anderson Taylor. William Clark was clearly a son of Spencer and Milly Atkins, and it appears that Madison and Anderson Taylor were sons of Benjamin. Others have said that this particular Benjamin married Rhoda Howell and that Madison and Anderson T. were two of their (probable) 13 children.
William Clark's children, including James Spencer moved on to Texas after that.
I would like to find information that Spencer, himself, could have been a son or sibling of this Benjamin, but I cannot find any evidence that this is so. This Benjamin is said to have been born in VA in about 1794, the same "about" date as the birth of Spencer.