I am researching my grandmother's ancestry as I am trying to prove UK ancestry for myself for work purposes.
Also in 1911 the family is listed on the English census:
James - 56 2855 Domestic Gardener Tarraby, Carlisle, Cumberland
Wife Mary - 49 1862 Papcastle, Cockermouth, Cumbria - http://en.wikipedia.org/wiki/Papcastle
Married 29 years. 10 Children born 9 living/1 deceased by 1911.
Children on census with them:
Constance daughter 15 1896 Aspatria, Carlisle, Cumberland
William son 13 1898 Aspatria, Carlisle, Cumberland
Henry son 11 1900 Aspatria, Carlisle, Cumberland
Living in Hindrigg, Aspatria, Carlisle.
This matches your 1901 and the ship info.
Aspatria Info - http://en.wikipedia.org/wiki/Aspatria
There's a "Jas" Mitchinson listed on the following ship from Liverpool to Saint John NB. Looks like your relative. List as age 59, Gardener.
Ship Name; Hesperian
Date: 26 March 1913
Liverpool to Halifax/St John, New Brunswick
He's one of many gardeners on the same page - not with wife or children.
Hope this all helps!