Hi Seamiuse,
It appears that you are doing this a long time, and most likely know the following, but I shall type it up just in case.
In the time period that you are referencing the church has very few burial records for. I have read numerous accounts on this which give varying reasons, the main seem to be that records wouldn't be written up 'til fees were paid, and sure with major poverty around fees often weren't paid. How true this is I don't know, but may explain the shocking lack of burial records.
The article below may be of some help, which states that very few Roman Catholics churchs have maintained burial records
irish church records explanationIn one branch of my family in rural Galway, I was amazed to look through their church records and find so few burial records for my family in their books. I know for a fact that they lived, died and would have been buried in the area but there were only a handful of them to be found. What was surprising (or not - depending on how you look at it) was that those that WERE found were mainly on men, very few women, and even less children. What women were recorded, most were written as Mrs....no christian name given.
Again with graves, it would seem that, unless you had a few bob, you would have been buried but very few had a headstone.
I have family that were buried as late as the 1950's and were not given headstones.
You have mentioned that Anne emmigrated about 1889, which would have made her about 15, fairly young. It MIGHT suggest that she was orphaned about this age.
I presume that you have looked for death certs for Patrick and Mary for this time period. Although they could have passed away when she was younger and she may have been reared by relatives.
As I said, you most likely know all this, but it might be of some help.
Tara