Thats him in 1901. daughter Amy 15 is a servant in Rugby in 1891 but no sign of John or the rest of the family.
The only two children accounted for on 1891 censuses are
ARNOLD, Amy Servant Single F 15 1876 General Servant Domestic Rugby
and
ARNOLD, Arthur J Boarder Single M 21 1870 Leather Dresser Montreal Canada
The family are not with their grandparents in 1891
1891 Village, Willoughby
ARNOLD, George Head Married M 76 1815 BadbyNorthamptonshire
ARNOLD, Hannah Wife Married F 75 1816 Kineton Warwickshire
A possibility for Frederick birth date & place of birth not correct
1891c Head William ARNOLD wife Kate
ARNOLD, Frederick Nephew Single M 10 1881 Scholar
? LondonWhen did John's wife Jane/Janet ARNOLD die ?
As John remarried in 1895 to Charoltte BROWN the daughter Lilian ARNOLD born 1891 Rugby living with them on 1901c and there's a son Charles born 1882 Rugby. Perhaps Jane died during of after child birth of Lilian.
Could John have taken some of the family to Canada for a sort time as this was Jane’s place of birth and then returned home alone
Have looked at later censuses for William born Canada & Frederick ARNOLD 1878 Rugby & but nothing.
The girls Sarah 1874, Amy 1878, Florence 1880 & Lilian 1891 could be married on later censuses.
Possible marriages for the boys
Marriage 1901 RugbyWilliam ARNOLD names on same page
Louisa CHIPMAN
Ellen MATTHEWS
Marriage 1907 RugbyCharles ARNOLD names on page
Maud Mary SOUTH
Annie WHISTON
The BROWN family seem pretty elusive on 1891 census too
Charlotte BROWN 1852 Oxford
Lucy 1887 Rugby
Maggie 1888 Ruby