Its challenge so I hope you dont mind me still continuing by collecting facts and hypothasising.
Hence I use terms like 'BELIEVED to be!'
Re
In 1891 there was
William H Grahams b.1880
Louise Funnell b.1877 (in law)
Ada Grahams b.1888
Jimmie Grahams 3 months old
All born in Brighton, Mercy Funnell is listed as a mother in law (birth mother?) and born in Lewes, in 1857.
George Funnell, a 38 year old general dealer (would that have been a traveller?) appeared in Brighton on the 1881 census with wife Mary and her daughter Louise. George is BELIEVED to have only just married Mary (BELIEVED to have officially been Mercy ANNIE Turner) in Brighton in the June quarter of 1881. Her daughter Louise or Louisa's birth to Mercy Turner, single mum appears on the IGI as born 10 Oct 1876 baptised Lewes 14 Jan 1877. But there is no birth of a Louise or Louisa Turner in Dec quarter 1876 of FreeBMD. So Louise's birth may be in a place not yet on FreeBMD, went unregistered, or appears under the surname of her unknown father.
It is BELIEVED George died aged 41 in Brighton in the March quarter of 1884 and Mercy found a new partner who was another General Dealer (traveller?) called William Grahams, Grimes, Graines or other varients of that name. Mercy & William Grahams are on the 1891 census living together (where?) but it is not thought they were actually married. They did that in Lewes in 1899.
The 1891 census above therefore suggests that both brought children from their previous relationships into the family and they then had two or at least one further child (called Jimmie or James) together.
I'm positive
William H Grahams was William Henry Graimes (Birth reg Brighton Dec quarter 1880)
You should buy copy of this birth cert
Louise Funnel was Louisa Turner appearing on the IGI as born 10 Oct 1876 & baptised Lewes 14 Jan 1877.
I believe
Ada Grahams (b 1888) may have been registered in Brighton in the June quarter of 1887, but as Ada Funnell.
And Jimmie could either be James Edgar Turner (reg Lewes Mar quarter 1891) or James Friend Funnell (reg Lewes Dec quarter 1890)
So on the 1891 census:
Check out Ada Funnel B c1888 Brighton. Finding her elsewhere disproves the first belief above.
Check out the two James' born Lewes on the 1891 census in order to eliminate the one you do find.
Finding both disproves the second belief above.
Note; Sometimes birth places and places of registration do vary. (for example, I have had a birth officially registerd in Brighton for a child whose actual place of birth was recorded as at an address in Kent)
Final note
No idea whether there is a connection, but the 1901 census has a 7 year old Florence Graham born Brighton but living in Hove.
Roy G