Nell,
Well, I flushed you out into the open at least!

You're right that I'm still doing a lot of speculation. The main problem I've got is that I'm trying to combine information from two living, but elderly, members of the family, whose only apparent thing in common is a firm conviction that the other is confused. There appears also to have been congenital disinformation within the family, such that parents have often been at best economical with the truth to their children as far as their own heritage is concerned. Obviously, I'm also struggling because I have no census data after 1901 and insufficient detail to get much out of the BMD index sets.
Thus, I have the following facts:
1. Widowed Walter Charles Snook (1861-1949) was at a hotel in Southampton on census night in 1901.
2. Two of his children were chez Broomfield in Boldre - it now looks as though the other two were at different addresses in Sholing (does "boarder" suggest some sort of fostering arrangement for the 8-year-old Aggie?).
As to the unsubstantiated family tittle-tattle...
Walter Charles Snook was a tenant farmer at Dunsford Farm, Boldre, "when his family were young". [If this is the case it must be between 1891 and 1901 - though I don't know how a yacht steward managed to turn his hand to farming.] At some point they moved back to Lymington, where Annie died (1899). They lived with a great aunt (?), Priscilla Broomfield, nee Perkins (?), landlady of the Wheatsheaf and husband of Alderman Broomfield, local bigwig, mason, etc. [There are plenty of old photos in the family of the Alderman, so I guess he must play a role somewhere!]
The biggest mystery is actually the identity of someone called "Uncle Len" of Warborne Farm Cottage, Boldre. One of my "convinced" sources says he must be William Henry George Snook (b. 1890, at Boldre in 1901 but apparently non-existent again until his death in 1962), while the other claims he is Leonard Tapp, who may have become part of the family through Walter Charles Snook's subsequent marriage(s) [which I can't tie down either]. They agree that he married Daisy and probably had 3 children, Robert, Edwin and Mary.
I appreciate that much of this is incredibly vague - I was simply hoping that you might be able to help me to establish some real facts and possibly open up some new directions...
Be gentle with me!
Cheers,
Brian