Toni,

I think you've concluded the correct thing. That this was some sort of temporary foster care setup. Possibly, Willie and Hester's mother died and their father, a coal miner, could not care for such young children. Byron Wolcott is married and his wife Sara and son are listed as living with Sara's parents the Cox's also in Cabell County. By 1910, Willie is listed in Winifrede Hollow, Kanawha County, with her father Augustus and his new wife of less than 1 year, Florence. Joseph is boarding elsewhere in Winifrede Hollow. The 1920 census indicates that Joseph and Willie married between 1910-1912. Don't think you'll find any marriage records online marriage records for Joseph and Willie. You'll need to contact the Clerk of the Court for Kanawha County. I did find this and it might explain why Willie and Hester were in Cabell County in 1900. Possibly, their mother was from Cabell County.

Name: AUG. L. CHAPMAN
Spouse: JENNIE BALL
Marriage Date: 28 Apr 1887
County: Cabell
State: WV

Source Information:
Dodd, Jordan, comp.. West Virginia Marriage Records, 1863-1900 [database on-line]. Provo, UT, USA: The Generations Network, Inc., 2000. Original data: See Description for original data sources listed by county.