Hi
I have been looking for the Perry family in the 1871 census: it might have included James b. about 1836 in Northumberland, Mercy b. about 1839 in Somerset, Jane b. 1859, Maria b. 1861, Ann b. 1867, Maria b. 1870 plus any other children born between the birth of Maria 1861 and Maria 1870. I have looked for Perry, Percy, Berry and Ferry plus Per* and also for Mercy, the two Marias and Jane without surnames but with the appropriate birth data. Search on A******y seems to be a little more eccentric than usual but I think that it has covered the ground and not found an 1871 record for the family. So perhaps they have indeed been missed.
If you want to know James's occupation and where in Trimdon Mercy was living in the second half of 1870 then you need to apply for a copy of the second Maria's birth certificate. The GRO reference from Freebmd is Births, Jul-Sep 1870 Perry Maria Stockton 10a 132 (Trimdon was in the Stockton registration district).
You could get similar information for Hetton in the first half of 1867 from Ann's birth certificate, reference Births Apr-Jun 1867 Perry Ann Houghton 10a 427.
All the best
Gobbo