As a fellow Caddick researcher who is aiming to link as many Caddicks as possible by assembling Caddick family trees from around the world, I think I have some information that might help you in your search.I have transcribed all of the Caddick birth, marriage and death registrations from 1837 to 1930 and cross-matched many of them.
Adelaide was born on 3 May 1863. Her birth was registered in Jun 1863, West Bromwich, Vol 6b, page 659 (GRO Ref) and Oldbury (OLD/32/381) as the local reference.Her parents are listed as Hannah HARPER and Elisha CADDICK (GRO Marr Ref Jun 1855, Dudley, Vol 6c, p149).She married in Burton-on-Trent on 19 Nov 1884 (to Peter George LINGS) and died on 2 Jun 1944.In the 1881 Census (Oldbury Pit Lane) she was registered as a "Dressmaker" - Hannah was registered as "Head" as Elisha is not shown at the family home.However, there is an Elisha Caddick (aged 47, Married, a "Cooper", recorded as lodging at the Shoulder Mutton 57 & 58 Hawkins Lane, Burton-on-Trent) and I believe that this might be Adelaide's father, especially as Pamela (below) seems to have married into a publican family).
Anyway, I hope that this helps.I have added the bones and details of this proposal into a family tree and would love to add your details if you are willing :-)
Thomas's birth was registered in Jun 1867, West Bromwich, Vol 6b, page 726(GRO Ref) and Oldbury (OLD/39/335) as the local reference. On 1881 Census aged 13.
Herbert's birth was registered in Mar 1859, West Bromwich, Vol 6b, page 595 (GRO Ref) and Oldbury (OLD/25/354) as the local reference (actually 1858).Not on 1881 Census.
Alice's birth was registered in Dec 1869, West Bromwich, Vol 6b, page 664 (GRO Ref) and Oldbury (OLD/43/322) as the local reference. On 1881 Census aged 11.
There are 2 possible references to Pamela, although the first, and indeed most likely) suggests that she was born shortly after her parents were married (Jun 1855, West Bromwich, Vol 6b, page 394 (GRO Ref) and Oldbury (OLD/19/494)), the next is in 1860 (Jun 1860, Dudley, Vol 6c, page 71 (GRO Ref)).I will endeavour to find the family in the 1871 census as the only Pamela in the 1881 Census is registered as a General Servant aged 19 (ie the latter registration). I have a record of Pamela Caddick marrying Thomas Underhill on 18 Feb 1879 in the Independent Chapel Oldbury.The couple are shown on the 1881 Census at Henry St, Oldbury, Worcester, England with 2 children (Ada aged 1 and Thomas aged 5M).Pamela is recorded as being 15 and a dressmaker which seems to fit the family trade.