Ah I was just thinking if the only known family detail we have is the brother in 1891 then perhaps his marriage certificate would help as other family even Margaret might be witnesses. I once picked up a ggm sister's married name as she was witness at ggm wedding.
So Frances A on 1891 born IOW Hampshire and a 1 yo child in 1891 must point to them being this one
Marriages Mar 1889 Alverstoke 2b 757
Anderson John
BARNES Henry
Cook Sarah Ann
Dunford Frances Annie
and sadly in 1901 she is a widow - a cook at workhouse
Frances Ann Anderson abt 1863 Iow, West Cowes, Hampshire, England Servant Easebourne, Sussex
John's marriage cert may well help
Back to Mrs James Anderson if you feel she might be woman you want
The 1891 has these children
C M Anderson abt 1885 Lka, London, England Daughter
M F Anderson abt 1887 Bayswater, London, England Daughter
M E Anderson abt 1889 N Kensington, London, England Daughter
not with parents in 1901

? perhaps at boarding school
Note: CM born Lka is a nonsense she was born India Ceylon perhaps a transcriber wanted to put Sri Lanka
So that does indicate James and Margaret married in India.
Looked for births for other two as you might want to purchase a cert to see mothers maiden name
Births Jun 1887
Anderson Mary Forrie Paddington 1a 21
Anderson May Florence Pancras 1b 181
Births Sep 1888
ANDERSON Maud Ella Kensington 1a 74