I think that the major problem is finding out if the daughter Mary kept the name Smith which the family were using in 1851 or reverted to Archer.
I assume from what I can work out that Mother Mary married Thomas Smith in Stratford, Dec.Quarter 1849. In 1851 the family, with the exception of William Jnr. were living at Milton Row, Old Stratford, all called Smith. Did William Jnr. die as well, there were, two deaths in Stratford? as he is not with them in 1861 either. In 1861 Thomas Smith 31, Mary Smith 42, and James Smith 13 are at No7, 4 Court, Aston, with no sign of Mary.
You say that Mary stayed in Stratford, what evidence do you have for that? As by the age of 16 it was not unusual for a girl to have left home and be living with a family as a servant. She could just as well be doing this in the Aston area as in Stratford. If she was calling herself Smith then it would be extremely difficult to locate her and trace any future marriage.
There is however a 19 year old Mary Archer, servant in Stratford in 1861 and a 16 year old Mary Smith. There are also possible marriages in Stratford for Mary Archer, but only a copy of the certificate will tell you if it is yours.