Sorry I was not able to find info on your Agnes Gooding but I was able to find their marriage date which might help clarify the siblings. And if you can find a death record for one of her children......just might luck out with her maiden name on it.
Looks like they did not marry until 1853.....IF her age is correct on the 1870 VA, Appomattox Co, census she was born about 1818..and 35yrs old at the time of this marriage. 35 is pretty old for a first marriage. So I wonder if Gooding was her previous married name or her maiden name. Just a thought.
Virginia Marriages, 1851-1929 Name: Joseph W. Driskill Spouse: Agnes Gooding Marriage Date: 19 Jan 1853 County: Rockbridge State: VA
From the 1850 VA, Charlotte Co census this may be Joseph W. Driskill's first marriage. His wife on this census is Frances A. Driskil
Virginia Marriages, 1740-1850 Groom Name: Joseph W. Driskill Bride Name: Frances A. Trent Marriage Date: 20 Dec 1843 County: Prince Edward State: Virginia
Ages on these old census records can be misleading but since I found Joseph with his first wife on the 1850 census you will see that Clem.....was on this 1850 census although he is shown as only 17 on the 1870 census. 1850 VA, Charlotte County Driskell, Joseph26 bn Charlotte (VA) , Frances A. 28 bn PA , William ?.5 bn Charlotte , Charles H.4 bn" , Littlebery2 bn" , Clement W.1 bn"
1860 VA, Botetourt Co indexed & written as BRISKER Brisker, Joseph35 , Agnes38 , Jas7 , ANN5 , John3 , Martha8months , Berry12 , Clementina 10 (here he is listed as female) All born in VA
1870 VA, Appomattox Co, Stonewall twp Driskill, Joseph W.49 , Agness52 , Charles H. 21 (Charles H. of 1850 census) , Berry19 (littlebery of 1850 census) , Clem W.17 (Clement W. of 1850 census) , Sarah E.15 , Ann14 , James L.12 , John A.10 , Martha J.8 all listed as born in VA.
I could not find Joseph or Agness on the 1880 census. But by 1880 census dau Martha J. is living with her married brother James L.......John A. is listed as a nephew, living with a Driskill relative.
If you go to Familysearch.org, the LDS site, you will find several names/addresses of others that have submitted info on this family group.With luck, you might be able to find some more leads on you Agnes Gooding. I also have a Gooden in my family line and the multiple spellings make them tough to track.