Clara appears on these two Censuses with her parents:
1850/ District of Columbia/ Washington
Lewis Thomas, 42y b.DC, occ: Packet Agent
Margaret, 25y b.VA
Laura V, 5y b.DC
Eleanor O, 4y b.DC
Clara E, 2y b.DC
Emma J, 4mos b.DC
plus one other

1860/ District of Columbia/ Washington
LEOUIS Thomas, 51y b.DC, occ: Wood ? Dealeer
Margret, 35y b.VA
Laura V, 15y b.DC
Ellenor, 14y b.DC
Clara E, 12y b.DC
Emma J, 10y b.DC
Milinda, 8y b.DC
Sidney L (m), 5y b.DC
Alfred H, 3y b.DC
Kate Mande, 1y b.DC
plus one other
residence: Washington City

Record of Marriage
groom: W H Parker
bride: Clara E Thomas
date: 26 January 1867
place: District of Columbia
“D C Marriages, 1811-1950”
FamilySearch

Clara appears on these three Censuses with her husband:
1870/ District of Columbia/ Washington
William Parker, 24y b.NH, occ: Int Rev Col
Clara E Parker, 22y b.DC
J H (m) Thomas, 34y b.DC, occ: Plasterer
residence: Washington City
(same residence as Margaret Thomas, 44y b.VA,
along with six children, all born in DC)

1880/ South Dakota/ Lawrence
h/ W H Parker, 39y b.Ireland?, occ: Atty at Law
w/ Clarra (sic) E, 31y b.DC
s/ Lewis N, 13y b.DC
d/ Clarra E, 9y b.DC
d/ Cora A, 5y b.CO
s/ William H Jr, 3y b.Dakota Territory
s/ Ralph, 1y b.Dakota Territory
residence: 127 Main, Deadwood

1900/ South Dakota/ Lawrence
h/ William H Parker, 54y b.May 1846 NH, M/33, occupation: Lawyer
w/ Clara E, 52y b.Jan 1848 DC, mother of 11/9 living
s/ Louis C, 32y b.Nov 1867 DC, occ: Miner
s/ William H, 24y b.Jan 1876 CO, occupation: Mine Surveyor
s/ Ralph E, 21y b.Nov 1878 SD, occ: Printer
s/ Logan A, 19y b.Sep 1880 SD, occ: Miner
s/ Theodore F, 18y b.May 1882 SD
s/ Clarence T, 16y b.Feb 1884 SD
s/ Francis F, 13y b.Oct 1886 SD
residence: (no house number) Forest Hill [Avenue], Deadwood

1910/ South Dakota/ Lawrence
h/ Clara E Parker, 64y b.DC, Wd, mother of 11/8 living, Own Income
s/ Clarence P, 26y b.SD
s/ Francis J, 24y b.SD, occ: Lawyer
residence: 13 Filmore Street, Deadwood

Link to son, Francis Joseph Parker. Sent edit to link parents 28 September 2019.

Links to two sisters, Laura Virginia (Thomas) Glenn, Eleanor Olivia (Thomas) Emerson and one brother, Sidney L Thomas. Sent edits to link parents 28 September 2019.

Link to sister, Honora “Nona” Gordon Thomas. Sent edit to link parents 02 October 2019.