Tara, Don't know if you are still watching this forum, but here is what I found:
Couldn't locate Josephine with the birth date you gave, but found her children in Marion, Jefferson County, Texas at website: www.familysearch.org. No images were available for these files.If you have Ancestry you might look up the children on there.
I did find a Josephine Fulton in The City of Wheeling, Ohio, Virginia.Maybe the city of Wheeling is close to the Kentucky state line and was considered Virginia back in 1854.Check your map for Wheeling, Virginia.It didn't list her ethnicity.
Josephine Fulton United States Census, 1860
birth: 1851 Virginia residence: 1860 , Ohio, Virginia
Name: Josephine Fulton Event Type Event Year Event Place Minor Civil Division The 4th Ward City Of Wheeling Age (Expanded)9 years Birth Year (Estimated) Birthplace Gender Page357 Household ID Affiliate Publication NumberM653 GS Film number805368 Digital Folder Number4298863
Maybe you can find some record for the children that will give you the information you are seeking (i.e. children's birth certificates, death certificates,.etc.).
Josephine Fulton in entry for Tennie Brown, "Texas, Births and Christenings, 1840-1981"
Name: Tennie Brown Gender: Female Christening Date: Christening Place: Birth Date: 08 Dec 1882 Birthplace: , MARION, TEXAS Death Date: Name Note: Race: Father's Name: George W. Brown Father's Birthplace: Father's Age: Mother's Name: Josephine Fulton Mother's Birthplace: Mother's Age: Indexing Project (Batch) Number: C59246-6 System Origin: Texas-ODM GS Film number: 1481605 V. 8-9 Reference ID:
Josephine Fulton in entry for Bonnie Brown Jenkins, "Texas, Deaths, 1890-1976"
Name: Bonnie Brown Jenkins Event Type: Death Event Date: 11 Jun 1974 Event Place: Jefferson, Marion, Texas, United States Gender: Female Marital Status: Widowed Birth Date: 18 Aug 1889 Birthplace: Marion, Texas Father's Name: George W Brown Mother's Name: Josephine Fulton Certificate Number: 44660 GS Film number: 2243200 Digital Folder Number: 005145135 Image Number: 01803
Josephine Fulton in entry for William Edward Brown, "Texas, Deaths, 1890-1976"
Name: William Edward Brown Event Type: Death Event Date: 21 Nov 1954 Event Place: Dallas, Dallas, Texas, United States Gender: Male Marital Status: Single Birth Date: 04 May 1880 Birthplace: Marion, Texas Father's Name: G W Brown Mother's Name: Josephine Fulton Certificate Number: 54016 GS Film number: 2114283 Digital Folder Number: 005145345 Image Number: 01695
Hope this helps if you have not already found the infro you were looking for.