So, as conclusively shown by Ladyhawk, the Ellen Wright - dau. of George and Martha - is not your Ellen Wright i.e. in 1891 'your' Ellen is with her husband Joseph William Davis whilst this Ellen is still single and living with her widowed mother Martha still in Yorkshire.
This takes us back to the other contender, 'shown as Nelly' in 1871 with George and Mary Ann (nee Howe). George was still single in 1861 so should have married between 1861 and 1871 - however, no trace of a marriage between this pair so looks like they never married. Young 'Nelly' bc.1862 was, I believe, born to Mary Ann late 1861/early 1862 and, if registered, birth would probably have been as 'Howe'. Can't see an obvious birth entry though and the next child of George and Mary Ann is Thomas Henry Wright, birth Dec.1868 mmn Howe some 7 yrs after 'Nelly' which suggests they probably didn't start living together until late 1860's. (It was not the marriage of George Wright and Mary Ann McKenna in Sept.qtr. 1868 as followed this couple).
I don't think that it was a coincidence that your Ellen married from Hedley Street where George and Mary Ann lived. I firmly believe that they were her parents and that in 1881 she is the Elen Howe, servant, born Sunderland in Bishopwearnouth (where her family lived).
I appreciate you want definitive proof but this family were somewhat unconventional in that parents didn't marry, and Ellen's birth not registered so don't think you are going to find written proof and only have the census to go by.
Annette