The IoM McCarthy family looks a fairly close fit to what you wrote in 1987. The "gardener" is correct for her father - he wasn't recorded as a publican until the 1861 census, and could have been after Mary had left the IoM - if she was the assisted immigrant aged 18, Sept 1857, on the "Chance"? Or because her children's birth regts didn't start until 1861 she could have been an unassisted passenger: MCCARTHY MARY 21 NOV 1859 OCEAN CHIEF B 170 002;
MCCARTHY MARY 20 SEP 1860 WANATA B 181 003?
It would be worth checking these three entries.

As you say, death certs with details given by a relative were often a bit wrong, which could account for her father's forename.

If her parents and elder siblings came from Armagh Ireland this could be why she gave this as her birthplace when registering her eldest children - perhaps her parents and grandmother talked about coming from Armagh while she was growing up. (Censuses: their birthplaces b.Ireland.) Then later she consistently wrote that her place of birth was Isle of Man for the last four children. Perhaps someone from home corrected her?

Giving Glenallay as her birthplace is interesting, and also naming their farm Glenhallen, Glenhellen, or Glenaulin. One census has her b. Castletown, and we know from censuses they were living in Malew, but moved shortly afterwards because the next children were b. German. Could this name have been remembered from where her father was working in Malew, German, or Onchan as a gardener?

Someone living in the IoM might suggest a place?

Sue