Can't see a marriage, but William and Elizabeth appear to split up some time in the 1860's and William appears to be living with his parents in 1871.
Elizabeth is living as a Housekeeper to a John Barrett in 1871, down as married, and with the 2 yougest Stewart children with her.
There is a marriage of a John Barrett and Elizabeth Stewart, formerly Shackleton 1874 on Durham County Coucil website.
John Barrett and Elizabeth are married in 1881 with 2 more children.
Meanwhile this looks to be William with his parents in 1871, he is down as a widower in 1881.
1871, Emma Pit, Auckland St. Helens,
Williiam Steward, 76, Furnace Minder, b. Bishop Auckland,
Elizabeth ", wife, 68, b. West Pits,
William ", son, married, 42, b. West Pits,
Jane A. Musgrave, Gdaur, 16, b. Auckland St.Helen,
+ some lodgers,
RG10/4927/40/36
So this looks to be William with his parents in 1841 :
1841, Burbeck Square, Auckland St. Helen,
William Stewart, 35, Coal Miner, Y
Elizabeth ", 30, Y,
Margaret ", 15, Y,
William ", 13, Y,
Ann " 9, Y,
Mary ", 7, Y,
Elizabeth ", 1, Y,
HO107/307/2/13/21
Assuming this is the right family William Senior is 52, b. Bishop Auckland in 1851, 65 b. Bishop Auckland in 1861.
The Elizabeth aged 1 on 1841 has mothers maiden name Mason on the GRO.
William Stewart married Elizabeth Mason, Auckland St. Andrew 18 Oct 1823, both of this parish.
Alan.