Hi Steve,
Seems SP has that "NEW" family as KERR.
But the father here is a George, not a Thomas...

--
GEORGE KERR
JANET DICK
Marriage: 22 JUN 1860 Bothwell, Lanark, Scotland
~some children~
JANET KERR - Birth: 14 AUG 1860 Shotts, Lanark, Scotland
CHRISTINA KERR - Birth: 17 FEB 1862 Cambusnethan, Lanark, Scotland
WILLIAM KERR - Birth: 16 APR 1864 Shotts, Lanark, Scotland
ROBERT KERR - Birth: 01 APR 1866 Shotts, Lanark, Scotland
GEORGE KERR - Birth: 08 FEB 1868 Shotts, Lanark, Scotland
MARION JANE DICK KERR - Birth: 07 JAN 1870 Shotts, Lanark, Scotland
MARY KERR - Birth: 09 AUG 1872 Shotts, Lanark, Scotland
ALISON KERR - Birth: 30 APR 1874 Shotts, Lanark, Scotland
--
1861 census 655 Ed 16 p 4 (Shotts)
Wester Rosehall.
George KERR, head, 30, Grain Cattle Dealer, b Whitburn, Linlithgowshire
Janet KERR, wife, 19, --------------------------b Bothwell, LKS
Janet KERR, daur, 8mos, --------------------b Shotts, LKS
Alice DICK, sis-in-law, 8, Scholar, b Bothwell, LKS
Marion THOMSON, servant, 13, Dom. Servant, b Shotts, LKS
--
Jack
====
ps later - I know you have the 1871, it's just to compare.
And perhaps father George has remarried by 1881?
--
1871 census 655 Ed 9 pp 36-37 (Shotts)
Brownhill.
Janet KERR, wife, marrd, 29, Farmer's wife, b Lanarkshire.
Jessie KERR, daur, 10, --------------------b Shotts, LKS
Christina KERR, daur, 9, Scholar, b Shotts, LKS
William KERR, son, 7, Scholar, b Shotts, LKS
Robt. KERR, son, 5, Scholar, b Shotts, LKS
George KERR, son, 3, --------b Shotts, LKS
Marion J. D. KERR, daur, 1, b Shotts, LKS
Alex. McLAREN, servant, 22, Ploughman, b Perthshire
William FISHER, servant, 17, Servant, b Calder, LKS
Isabella BISSELL? servant, 21, Servant, b Motherwell, LKS
Sarah DOCHERTY? servant, 14, Servant, b Shotts, LKS
Thomas BLICE? servant, 74, Servant, b Ireland
--
1881 Census 655-2 EnumDist 4 Page 5 (Shotts)
Brownhill Farm
Margaret KERR M 30 F Cairnehead, Lanark, Scotland Rel: Head Occ: Farmers Wife
William KERR U 16 M Brownhill, Lanark, Scotland Rel: Son Occ: Employed On Farm
Robert KERR U 15 M Brownhill, Lanark, Scotland Rel: Son Occ: Employed On Farm
George KERR 13 M Brownhill, Lanark, Scotland Rel: Son Occ: Employed On Farm
Marion KERR 10 F Brownhill, Lanark, Scotland Rel: Daur Occ: Scholar
Mary KERR 8 F Brownhill, Lanark, Scotland Rel: Daur Occ: Scholar
Alison KERR 6 F Brownhill, Lanark, Scotland Rel: Daur Occ: Scholar
Isabella KERR 5 F Brownhill, Lanark, Scotland Rel: Daur Occ: Scholar
Jessie KERR 1 F Brownhill, Lanark, Scotland Rel: Daur
Isabella WHITE U 23 F Sanquhar, Dumfries, Scotland Rel: Serv Occ: General Servant
Ellen WILLIAMSON 12 F Beeches, Linlithgow, Scotland Rel: Serv Occ: Nurse
William DICKSON U 21 M Bathgate, Linlithgow, Scotland Rel: Serv Occ: Farm Servant
====
So a transcription error by Ancestry saying the surname in 1871 was NEW - should've been KERR.
Sorry, not what you wanted to hear...
What censuses do you have for William New?
====