Ok, just to clarify and possibly summarize…
I know that her name is Mary J Graves, born to Isaac Graves and Jane Bracey.
I have her in the 1851 and 1861 St Woollos(Newport) censuses living with her parents and siblings.
Assuming the J is in fact Jemima, then it's safe to say that she married Alexander Fulham Parsons (B:1847 in London; D:1872 in Newport) in 1868.
In 1971 census, I have a Mary Parsons (correct date/location of birth) married to Alexander Parsons, and their child Alice Parsons. They are living in Christchurch, Monmouthshire, Wales.
Post 1971 is where it seemed to get a bit fuzzy:
Mary Jemima could have married a Robert Pugh in 1878 in Newport, which would match a 1881 census of a Mary Pugh, wife of Robert Pugh, and mother of Alice M. Parsons (listed as step-daughter to Robert). They are living in Abergavenny. This seems like the most likely possibility.
However, I also found a Mary Parsons listed in an 1881 census for St Woollos (Newport), Monmouthshire. She is listed as married, but head of household w/ no one else listed. The birth year/place also work, and she was born in this area. This second 81 census threw me at first, but I guess there must have been another Mary born in Newport about the same time who married a Parsons.
Also, this all depends on whether this Mary Jemima we are discussing is the correct Mary J, daughter of Isaac Graves and Jane Bracey.
Thank you for all your help. This is fantastic!