Bill
Hello, I don't know if you ever got to the bottom of this, and I am afraid I can't shed a great deal of light on it for you, but I am related to some of the people mentioned in your original message.
Herbert William Rands (1885-1938) (known as Bert) was my great-uncle. He was the brother of my grandfather, Edgar Smith Rands (1897-1986). Bert's daughter Elizabeth Begbie Rands (1910-2002) (known as Lily) was known to me. Her married name was Davison and she was (obviously!) a cousin of my father, Trevor Edgar Rands (1933-2014). I was born in 1968.
Lily never talked to me about her mother but I do recall my grandfather saying that Lily's mother was a Revell and had left Bert when Lily was very small. Lily had a brother, Samuel Revell Rands (born 1905), and I had noticed the reference on Bert's 1911 census entry that he had had another child who had died.
Bert subsequently moved to London and remarried and died at Homerton Hospital in 1938, aged 53.
By searching on Ancestry I established that on the date of the 1911 census Samuel, aged 5, was a "visitor" at the address of two sisters, Martha Carmichael (age 54) and Alice Carmichael (age 50), at 21 New Bridge Road in Hull. Samuel's name was wrongly recorded on the census form as "Samuel Nevill Rans" but the Ancestry search engine is clearly intelligent enough to have located it!
My great-grandmother, Louisa Catherine Rands (1860-1943), with whom Bert and Lily were living in 1911, decided in the 1920s that Lily was going off the rails and sent her to London where she spent several years in service, before returning to Hull in the 1930s to get married.
Samuel Revell Rands is also interesting because Lily and my grandparents all said that he had disappeared at some point in the 1930s and they never saw him again. From my research on Ancestry I have established that he got married in Kent in 1939 to someone who died as recently as 2005 and they had two children who went on to have children of their own. I have not yet however managed to establish when Samuel lived until or what happened to him.
Anyhow, that is more than enough rambling and I hope you managed to solve your mystery. I would be interested to know if you did manage to find out more, and would be similarly happy to share any useful information I have with you although, as I said above, I am not sure that I can be a huge amount of help!
Kind regards
Edward Rands