Okay so the census reference for 1901 is Piece 4713 Folio 200 Page 56
John Wright, head, 29, Insurance Agent, born Sunderland
Margaret Wright, wife, 25, born Sunderland
Sarah J Wright, daughter, age 2, born Sunderland
We aren't allowed to do look ups for the 1911 census, but if you have access to it, and that too says he was born in Sunderland, then could you tell us where the info about him being born in Bishop Auckland came from? The 1911 census would also give you the number of years since they were married, which would help to narrow down the certificate search.
I am not saying your info about his birthplace is incorrect, the 1901 census has the birthplaces 'dittoed' so that may be the incorrect place, but the 1911 would have been info given by him so is more likely to be right (if that makes sense)
Given Sarah J's age, they were likely married in the late 1890s, I have looked on FreeBMD for a John WRIGHT marriage to a Margaret Patterson and can't see one. Always an outside chance that Patterson was her birth surname but she may have been a young widow when she married so would have been in the register with her previous married name.
The only possible Agnes A Wright I can find a birth registration for was in Tynemouth District Q3 1910 (via Free BMD) I can't see another Agnes (A) Wright born in the North East in the period 1910-1912.
I assume that one of their children (? possibly Agnes) is your direct ancestor, do you have any documentary evidence of her being born in 1911 (birth cert, baptism etc?)
Sorry to answer your question with lots more questions, but often we have to explore all possibilities before we can be sure that we have found the correct ancestors. Between us all (experience of people in here in looking, added onto to what you know about your family history from older generations) will get you there in the end, but we need to pool the info :-)
Boo