I think I may have found William and Esther on board a vessel called the Flat John on the 1861 census.
William Vernon, married, 33, master, born Liverpool
Jonathon Vernon, widower, 55, mate, born Northwich, Cheshire
Esther Vernon, married, 23, wife of master, born Sutton, Lancashire
(Piece: 4506; Folio: 220)
On the 1871 census in Warrington is:
Esther Vernon, wife, married, 32, waterman's wife, born Lancashire, Ashton
George Vernon, son, 9, born Lancashire, Warrington
Mary Ellen Vernon, daughter, 6, born Lancashire, Warrington
Margaret Vernon, daughter, 4, born Lancashire, Warrington
Amelia Vernon, daughter, 1, born Lancashire, Warrington
Esther Lee, sister, married, 36, born Lancashire, Warrington
Ada Lee, niece, 2 months, born Lancashire, Warrington
(Piece: 3903; Folio: 22; Page: 1)
Esther Lee is actually Esther's sister-in-law. There is a marriage for Esther Vernon in Warrington in the 3rd quarter of 1863 that has a Joseph Lee on the same page (vol 8c, page 155). This family certainly matches up with the one JJ found on the 1881 census.
I think the 1881 census that had Annie Vernon listed with the surname Harper was a mistake by the enumerator when transcribing the census. It is certainly possible he got over-zealous with the ditto for the surname and relationship.
Jacquie