As divorce was not really obtainable for the average person, it wasn't unusual for couples to simply go their separate ways and later live with common-law spouses instead of officially remarrying. Probably easier to explain her away as illegitimate than to admit she wasn't married to Frederick.
Although it's not clear exactly what happened or what age Adelaide was at the time (if the 1891 census is right, she was close to 16 at Adelaide Jr's birth), it does look as if we might have:
May 1880: Thomas Hilleard/Hileard, son of Richard, m. Adelaide Andrews (a copy of this record should give Adelaide's age, although she may well have lied about it).
April 1881 (census): Thomas Hilleard, pipe maker, son of Richard, in Bermondsey (single)
June 1881: Thomas Hillyard, pipe maker, and wife Adelaide, baptised a daughter, Adelaide Elizabeth (Thomas might not have been involved, of course, Adelaide could have given the details).
Although Adelaide Elizabeth could have born earlier than June - I cannot see a birth registration for her.
Thomas might be the same pipe maker who later turns up in Bermondsey as living with a Julia with a number of kids - this family also use multiple spellings, Hilleard/Hileard/Hilliard. Funnily enough, I can't seem to spot a marriage for this pair either.
Cannot find daughter Adelaide in 1901, either. Can she be spotted on the school records under some variation of Hilleard or Andrews, perhaps? It would be good to find some confirmation that the child Adelaide Hil*rd is indeed the same as the Adelaide who appears in 1891 with Frederick Liffen's family. At the moment I'm classing it as "likely hunch".
