Ooohhh you've got me questioning my whole research now!!!
If I go backwards with what I have:
Shadrach Wright married Isabella Highton 8th April 1875 St Cuthbert, North Meols son of Henry Wright a Labourer witnesses William Wright and Marintha Highton.
Announcement in Southport Visitor - WRIGHT-HIGHTON April 8th at St Cuthbert Church, Churchtown by Rev E H Thomas Shadrach second son of Mr Henry Wright late
leading stoker on HMS Warrior to Isabella eldest daughter of Mr John Highton builder Churchtown
so 1871 census Shadrach boarding with brother Reuben in Railway Street, Southport no parents or brother William - didn't have access to Ancestry when I started on Wrights didn't find them locally.
1861 Alice Wright married living with Robert, Shadrack and William with Thomas and Esther Leadbetter in Mount Street, Southport Detail: Class: RG9; Piece: 2761; Folio: 106; Page: 24; GSU roll: 543025.
1851 Henry married to Alice living with in-laws in Burscough
Shadrach born 28th August 1852 Martin's Lane, Burscough, whilst Henry was on HMS Rodney at that time Henry was only Ordinary Seaman, Alice give's Henry's occupation as Boatman - she can't read or write.
Haven't got birth certificate for Reuben. I have also not found any baptisms for Reuben or Shadrach or any of the other children which also makes me suspect Non-Conformist. Alice was baptised at Churchtown Independant Chapel.
William Wright was born abt 1856 according to 1861 census but haven't been able to find him in any other census or marrying. I only found Thomas when I could search the 1871 census nationally with an index! He is supposed to have been born Southport in 1867. Then I only found out recently there was a further child - Elizabeth Alice buried in the family plot she was born about 1872 and died 1874. Alice must have got pregnant when Henry came out of the Navy!
As far as the names go - Reuben I haven't a clue! Shadrach was perhaps named after Alice's eldest brother. William ?? Thomas after Alice's father Thomas Leadbetter and Elizabeth Alice after Alice's mother and herself.
Though looking at his navy records with his list of ships I'm not sure as to how he could have fathered William and Thomas! He only had a day between ships
Rodney Ordinary Seaman 30/04/1852 30/01/1856 Crimea War
Pearl Stoker 31/01/1856 16/06/1859
Minotaur Leading Stoker 17/06/1859 09/07/1859
Clio Leading Stoker 10/07/1859 29/08/1863
Cumberland Leading Stoker 30/08/1863 29/02/1864
Trafalgar Leading Stoker 01/03/1864 16/09/1865
Orontes Leading Stoker 17/09/1865 22/01/1866
Forester Leading Stoker 23/01/1866 30/09/1867
Opossum Leading Stoker 01/10/1867 01/08/1868
Ocean Leading Stoker 02/08/1868 14/07/1869
The only marriage I could find for Henry Wright to Alice Leadbetter is the one at Manchester Cathedral.