Have just done a quick check on Findmypast re your GRADY family.
On the 1851 Census they are living in Bengall Street Manchester. The
Ecclesiastical District is St. George. Sub District Ancoats.
This is the family:
Patrick, Head ,Married, M, 35, 1816, Porter, Ireland
Alice, Wife, Married, F, 40, 1811, Bolton, Lancashire
Timothy, Son, Unmarried, M, 1838, Scholar, Manchester, Lancashire
Mary Ann, Daughter, 10, F, 1841, Scholar, Manchester, Lancashire
John, Son, Unmarried, M, 7, 1844, Scholar, Manchester, Lancashire
Anthony, Son, Unmarried, M, 12, 1839, Scholar, Manchester, Lancashire
This should settle your St. George query. Anthony's birth doesn't appear to
have been registered but it looks as though the others are if you use the
above years rather than the ones you have. I'll send you the actual
references if you want to send for the birth certificates.
The family are not showing in the 1841 census.