A chink of light, but as always, more work and info needed to be found

Getting nowhere so far on daughter Jessie, however.....
Following on the idea of Sydney Archibald and Jessie Holland may not have been married...there is a parish entry for the christening of a Sydney Holland in South Lambeth All Saints on 29 Jan 1897. The mother of this Sydney shows as a Jessie Holland, no occupation for the mother was included. The address given for this Jessie Holland is the same as that given for another entry above, also for an illegitimate birth (41 Jeffries Road, Lambeth) so maybe this was a place for unmarried mothers to have their babies? Don't know, just guessing.
A leap (of faith?!) to the 1901 census and this entry in Raunds, Northamptonshire (RG13/1454/35/61):
Arthur Adams 24
Ellen Adams 23
Winnifred A Adams 2
Frederick C Adams 1 Month
Frederick S Archbold 42, married, actor b. Shotley; Bridge, Yorkshire
Sydney H Archbold 5, boarder b. London
Robert Wakefield 28, boarder
S middle name maybe Sydney and H middle name maybe Holland...
Frederick shows as married above. Maybe young Jessie is with mother somewhere together?
Monica
