Fanny Kate PRIDHAM's birth was registered in September quarter 1853 in Llanelly registration district. Entry is currently missing from the 'new' online GRO Index so no mother's name is available, but judging by the entry for her younger sister it may be Morris. There is also a marriage in June quarter 1852 Llanelly registration district with a Thomas Pridham and a Sarah Morris on the same page. PR image availabe on FMP in Carmarthenshiire Marriages and Banns dataset.

1861 census reference RG9/4113 folio 34 page 4
Living in Llanelly.
Thomas Pridham, 50, chemist, with wife Sarah, 35, and children Fanny K, 7, and Annie E, 5.

1871 census reference RG10/5522 folio 16 page 6
Living in Steynton, Haverfordwest, Pembrokeshire
Thomas, Sarah, Fanny Kate, and Annie E, all exactly ten years older.

In September quarter 1880 Fanny marries Otto Hawker PARTRIDGE, Barton Regis registration district.

1881 census reference RG11/2476 folio 31 page 26
Living in civil parish of St Michael, Bristol
Otto Hawker Partridge, 24, income from money, born Orletory, Herefordshire. (Should be Orleton.)
Fanny Kate, 27, born Llanelly

Backtracking on Otto's history, his birth was registered December quarter 1856, Leominster registraiton district.
Can't easily find him in the 1861 census, but he may have been living on the Isle of Man.

1871 census reference RG10/5776 folio 8 page 14
Living Douglas, Isle of Man.
Richard Partridge, 40 annuitant, born England, wife Catherine 44, born Wales, Otto 14,born England, Catherine{?} Eveleyn 8, and Ann Amy 5, both born Isle of Man.

In 1888 Otto and Fanny emigrated on the City of Richmond, which arrived in New York on 28 May 1888, although Otto said his destination was San Francisco.

The story then picks up on pages 20 and 21 of

FMP has links to the 1901 and 1911 Canadian census images.
I haven't looked for Otto and Fanny in 1890 in America or 1890/1891 in Canada.

I have left postems on the birth and marriage entries on freeBMD, and have also advised the relevant FHSs of the two 'strays'.