Working on the theory that Clara may have been illegitimate I looked for a marriage in Dudley of a female with the surname Shipley and came up with this:
Apr-Jun 1887, Dudley, 6c / 94 - Sarah Shipley & Joseph Hill or William Roe
1891 Census - RG12/2279/17/27
George Shipley 66 Head b (?) Staffordshire, Ag Farm Labourer
Hannah Shipley 64 Wife b Yoxall, Staffordshire
George Shipley 15 Son b Oldbury, Farm Labourer
Sarah Row 37 Daughter Widow b West Bromwich, Brick Yard Labourer
Clara Row 5 Grand Daughter b Oldbury
Flora Row 3 Grand Daughter b Oldbury,
Mary Row 10M Grand Daughter b Rowley Regis
What do you think?
There is a birth for a Clara Jane Rowe in the Dec Q 1885 in Burton on Trent but I cant find her on the census - unless this is her above

William Roe, Labourer, of Newbury Lane, Oldbury, Worcs, died 31 Jan 1890 leaving an estate of £72. Administration was to his widow, Sarah Roe of Tividale, Rowley Regis, Staffordshire.
Added: In 1901 Clara Ro(w)e is still living in Rowley Regis (Dudley RD) in the home of George P Shipley aged 26. Clara is listed as his sister in law, aged 18 and a brick maker.
Also added: Just checking my registration districts, Oldbury - Clara Ro(w)e's PoB - came under West Bromwich, which ties in with the birth registration for Clara Jane Shipley.