I have virtually all the census data for all UK Stocks from 1841 census to 1901 census. There is only one 'possible' match. The 1861 census finds a John Stock (b 1831) married to a Hannah (born Hockley 1836). The only marriage that 'fits' [from Rochford registration district - for hockley] is that this John married a Hannah Sparrow. There is another marriage of a John Stock to a Hannah Bush elswhere in Essex but that one is much less likely. I have assumed the marriage would have to have been between 1851 and 1861.
At this stage, they have two children Mary (b 1858) and Louisa H ( b 1860).
1871 still finds them in Hockley, and Mary is missing. But there are extra children Alice (1862) John William (1865) Priscilla S (1868) and Margaret (1870).
By 1881, Alice and Louisa are both away from home as Servants, and two new children are evident. Charles (1875) and Augusta (1879)
1891 sees the arrival of "Ivyston" Stock (or similar) who is a grandson. Without getting certificates I cannot tell the parentage. He could either be an illigitimate son of one of the daughters, or John has got married. But John William has "disappeared" and I haven't been able to pick him up again. By 1901, John has died, and Hannah lives with young Ivyson. Charles has also died and Augusta got married. There is an 1868 "Anna" at home, who I can perhaps assume is actually Priscilla with an updated name (not uncommon).
What I can add, however, is that there is a marriage of a John Stock to Hannah Jones in Stourbridge - which is one of those that I just cannot tie up with any of the census data.
So I think we have three possibilites. (1) The Family outlined above has a strong Hockley connection. But other things don't fit. You will know better than I the "strength" of your information and whether it could be that John William went off to USA? I cannot explain where Hannah Elizabeth might come into it. [Other than a wild co-incidence that this John married a Hannah Jones and subsequently gave birth to a Hannah Elizabeth]
(2) A variation might be (especially if I have the right family above) that the Stourbridge marriage does in fact relate to this John & Hannah. [With such a large database of Stocks, I had to make assumptions in 'reconciling' all the family groups from one census to the next]. I 'plumped' for the Hannah Sparrow marriage because it is the right time and the right registration district. But it occurs to me that you mentioned a Welsh connection. Stourbridge is roughly halfway between Essex and some parts of Wales. If one were to hold a wedding to "even out" the travelling between an Essex and a Welsh contingent, then Stourbridge is as good a place as any. Clearly this scenario still doesn't explain Hannah Elizabeth.
(3) Your particular John Stock may well exist - and he married Hannah Jones in Stourbridge. If so, then all I can say is that they have "evaded" appearing on the census. This is not impossible, but I don't have any unaccounted-for John/Hannah Stock in 1861, nor 1871, nor 1881. I have reported corrections to Ancestry.co.uk on a massive scale - and I think I have found the majority of transcription errors. But obviously can't claim to have them all.
Perhaps obtaining a few of the marriage/birth certificates (at £7 a time) might be a good next step. Assuming you have the means to look up all the Volume and Page numbers yourself; but if not, please contact me.