Looks like a problem trio.
No Catherine on the 1911 census, and too many William Edwards on all censuses, so would need further details.
Only one Nelly on the 1901 census (a 24 year old spinner) but in Hove not Brighton.
Again lots of other William Edwards that could be her spouse, but if you go by associated proffession, the most suited would be a 44 year old cotton merchant from Lancashire also living in Hove. Cant find their marriage on FreeBMD though. (not uncommon with Steyning district on FreeBMD) The GRO has the full index which I cannot access on the Internet.
Suggest you get a copy of the 1906 birth cert, note the father's occupation and then try to find him and Nelly on the 1901 census. Follow that up with getting a print out showing the family as it was then and use those family details to locate them all in 1911.
Roy G