This dictionary references 4 painters of this period with the BROOKER surname. None of these are believed to be related.

BROOKER Harry fl 1876-1902 Painter of domestic genre, especially of children. Exhib. one picture at the RA and four at SS. His Victorian interiors and figures are full of period charm, and follow the tradition of Webster and F.D Hardy.
BROOKER E.W. Commander R.N. fl 1870 Exhib 'Nibu Karra, Inland Sea, Japan' at SS, 1870. London Address
BROOKER, Miss Catharine P. fl 1881-1893 London portrait painter. Ehib 1881-93 at RA, SS, NWS and elsewhere.
BROOKER. J fl 1857 Exhib. 'A Little Too Hot' at the BI, 1857. Bath address.