I found this family tracked them through census years :
1851 Census Fordington, Dorchester Dorset, 135 Mill Street
James Wells 35 b 1816 Broadwalke Wiltshire Razor/Grinder
Catherine 28 b 1823 Dublin, Ireland
James 15 b 1836 Yeovil, Somerset, Basket Maker
Fredrick 8 b 1843 Fordington, Dorset,
Alice 6 b 1845 Fordington, Dorset,
Sarah Ann 4 b 1847 Fordington, Dorset,
Edward 4mths b 1850 Fordington, Dorset,
+136 Mill street
Joseph Smith 48 b 1803 Southampton, Hampshire, Basket maker
Sarah 54 b 17 97 Teffont, Wiltshire
Julia 27 b 1824 Portsmouth, Hampshire
Mary Ann 6 b 1845 Portsmouth, Hampshire
Margaret 4mths b 1850 Reading, Berkshire
Joseph Robinson 22 b1829 Kingsland, Middlesex Shoemaker
Eliza Townsend 18 b 1833 Chebsey, Middlesex Visitor
Mark Noble 20 b 1831 Bath, Somerset, Tinman
1861 Census Fordington County/Island: Dorset Mill Street
James Wells 45 b 1816 Broad Chalke, Wiltshire, England Cutler
Kitty 36 b 1825 Dublin, Ireland
Fredrick 18 b 1843 Fordington, Dorset,
Alice 16 b 1845 Fordington, Dorset,
Edward 10 b 1851 Fordington, Dorset,
George 8 b 1853 Fordington, Dorset,
Amos 6 b 1855 Fordington, Dorset,
Eli 4 b1857 Fordington, Dorset,
Horace 3 b 1858 Fordington, Dorset,
Emma 1 b 1860 Fordington, Dorset,
1871 Census Fordington, Dorchester Dorset, Mill Street
James Wells 54 b 1817 Broadwinsor, Wiltshire, widow/Grinder
Fredrick 29 b 1842 Fordington, Dorset, Gas fitter
Mary Ann 25 b 1846 Fordington, Dorset, Sister in law
Amos 15 b 1855 Fordington, Dorset, Son
Eli 13 b 1858 Fordington, Dorset, Son
Emma 9 b 1862 Fordington, Dorset, Daughter
Elizabeth 7 b 1864 Fordington, Dorset, Daughter
1891 Census Lyme (Lyme Regis) Axminster Dorset
Matilda Stone 50 b 1841 Uplyme, Devon, Widow/licenced Hawker
John 30 b 1861 Lyme, Dorset
James 19 b 1872 Lyme, Dorset
Noah 16 b1875 Lyme, Dorset
Elizabeth 15 b 1876 Lyme, Dorset
Mary Jane 12 b 1879 Lyme, Dorset
Kate 9 b 1882 Lyme, Dorset
Alfred 8 b 1883 Lyme, Dorset
James Veach 55 b1836 Uplyme, Devon, Lodger/Labour
James Wells 90 b 1801 Bristol, Gloucestershire, Visitor widow/Licenced Hawker
Christenings :
Fredric Wells 30 Apr 1843 Christening Place: Fordington, Dorset, England
Father's Name: James Wells Mother's Name: Catharine
Amos Wells 11th April 1855 Christening Place: Fordington, Dorset, England
Father's Name: James Wells Mother's Name: Catherine
Eli Wells 12 Jan 1857 Christening Place: Fordington, Dorset, England
Father's Name: James Wells Mother's Name: Catharine
Horace Wells 31 Jul 1859 Christening Place: Fordington, Dorset, England
Father's Name: James Wells Mother's Name: Catherine
Emma Wells 14 Mar 1861 Christening Place: Fordington, Dorset, England
Father's Name: James Wells Mother's Name: Katharine
Marriage :
James Wells – Catharine Ryalley 1842 Jul/Aug/SeptSturminster Dorset
I wondered if it was your James Wells ? But couldn;t find Matilda ,then in 1891 there is a Matilda Stone ? and it looks like James Wells is visiting as you have marriage before 1851 Census could she be their daughter ?
I found a marriage
Matilda Wells - Henry Stone Jul/Aug/Sept 1858 Axminster Devon Dorset
It may not be your family but hope it helps someone
