Thanks JJ, so infant born and died 1882, buried Presbyterian, but our OP is sure that baby was illegitimate birth, although the NSW BDM birth and death cert lists her lawful husband as father of that baby... FOUR of the Minton children (of Thomas and Mary) were admitted to Destitute Asylum in 1877 and reclaimed in 1878 (both admit and reclaim by Thomas only, no mention of Mary) and their 'Religion' listed as Prot ... I am sure that is Protestant standard abbreviation on those Asylum records.... and now Thomas was not buried Roman Catholic, but OP has assured us that they were Roman Catholic as they married RC in New Zealand...
Very confusing, but basically our OP wants to find burial of Mary who gave birth to a baby girl at 20 Exeter Place, Sydney (off Elizabeth Street down Surry Hills end) in November 1882. Mary may have had an extra-marital with E T FOLEY, but I have not found anything to confirm that as yet.
Hope that covers the short version.

E Townsend FOLEY was transitted back to Townsville but seems to have returned to NSW by around 1880s... Perhaps had lease on the Old Domain Baths when it had a natural sand/beach base and boardwalks around perimeter for customers to jump/dive off into water of varying depths...
JM