Hi Susan
This puzzle seems to have been hanging in the air for over twelve months now so I made an attempt to help you out. I must say that I still ended up with more questions than answers.
Betsy:
I suspect that ‘Betsy’ was just a nickname that stuck and that she wasn’t registered as Betsy Moody. If her father was named as James Riley on her marriage certificate, you could look at the birth listings either side of 1850 for ‘Eliza’ and ‘Elizabeth’ Riley on
www.cheshirebmd.org.uk. There are a number of possible entries between 1849-1852.
Eliza/ Betsy and her children can be tracked through successive census returns right up to 1901, and I presume you’ve already found these ? Interestingly, husband George doesn’t appear on any of them.
Mary
Again, there are two possible birth records in the right year that you’ll find on
www.cheshirebmd.org.uk.
I might have found Mary Moody (age 17) in the 1861 census, lodging with a family called ‘Donohoe’ in Buckley Street, Stalybridge. Head of the household is Mary Donohoe, a widow aged 38, born Ireland.
There’s then a possible marriage for Mary to John Ross at Mottram in Longdendale, St Michael in 1866 (CE31/7/166).
If she did marry John Ross, there’s a possible 1871 census entry for her in Chorlton on Medlock. The husband's name is listed as 'James' but the next door family is 'Donohoe' so tghere might be some connection.
There's a possible emigration listing to Canada for Mary Ross later the same year. If she didn’t marry John Ross, there’s still a possible 1871 emigration listing to Canada for Mary Moody in 1871.
Eliza:
I think Eliza died at Dukinfield in 1890 (DUK/80/78) but as you say, she’s absent from almost every census except 1861-1871. In 1861, I think she’s living with daughter Betsy (listed as ‘Betty’) in Peel Street Yard, Stockport and we know where she is in 1871.
I found a court appearance listed at Chester Sessions in 1855 where ‘Eliza Moody’ was found not guilty of larceny but I’ve no idea whether this is your ancestor. There’s a similar listing for Joseph Moody in 1855 at Lancaster Sessions. He was given 2 months jail for malicious assault
I then found this comment on an Ancestry tree:
“1871 Census, she is shown as a charwoman, born in Ireland abt 1820. At this time she was a widow living with Edward born 1861 (subsequently found to have been fathered by Isaac Charlesworth and is Eliza's grandson) and daughter Mary born abt 1844, who was a cardroom hand. They lived at 103 Hampsons Yard Dukinfield. In the 1861 Census she lived at 4 Peel St Yard in the Pleasant Street area. Her daughter Betty was 11 and was a silk piecer. She does not appear in the 1881 census
The IGI Source batch C 393986 gives a Christening at Ashton for Mary Anne Moody on 7/9/1845. The father's name is John Moody and the mother is called Betty.”
If this information is correct, no wonder you’ve had a struggle to find these ancestors. There are copies of various certificates available on Ancestry trees and, to save buying them, if you can’t copy these yourself, I don’t mind doing it for you.
Hope this stuff helps you move forward