I don't think you need be overly concerned about the apparent inconsistency in Mary's date of birth. In 1841, the census shows her as 40 which (as ages were rounded down to the nearest 5 in that census) gives her a birth year of anything between 1795 and 1801. In 1851, the enumerator's book shows 32, but this is clearly the same family as in 1841, less father David who is now dead. In 1861 she is 62 and in 1871 73. So it is only the 1851 age which is wildly out. My guess is that this was a mistake on the part either of the person who filled in the form or the enumerator. It may have been a slip of the pen, but it may also have been the enumerator misreading a badly written 5 for a 3.
There seems to be a REDFERN connection, but there is no marriage that I can see between a David BRADLEY and a Mary REDFERN. But, as Eliza's younger twin sisters Ellen and Mary were (helpfully!) born after the start of civil registration, you can ascertain Mary's maiden name by getting one or other of their birth certificates. The GRO references (from FreeBMD) are:
Surname First name(s) District Vol Page
Births Dec 1838
Bradley Ellen Macclesfield 19 93
Bradley Mary Macclesfield 19 93
If you order the certificate direct from the GRO via
www.gro.gov.uk it will cost £9.25 including postage. Make sure you tick the yes box when asked if you have the GRO reference and only fill in the required (starred) fields when ordering.
This may seem like a lot of money, but it is a small price to pay to ensure that you don't go down the wrong path.
Best wishes
Caroline