The reason for this seems to be a strange confusion between geographical and political terms. PGC, however, just repeats what geocaching headquarters does:
Although the country name is "United Kingdom" effectively what they mean is "Great Britain". "Ireland" on the other hand for them is the entire island, not just the republic. That’s why Northern Ireland ends up under "Ireland". (There were a number of caches in the past which are in Northern Ireland and were attributed to "United Kingdom" without specifying any level 2 administrative unit ("state"), but all of them have been archived in the meantime.)
Of course, all this does not make a lot of sense. I see the following solutions:
a) Convince headquarters to include Northern Ireland into "United Kingdom". However, in this case they would need to split the 2nd level ("state") unit "Ulster", because there is, of course, a difference between Ulster and Northern Ireland, as only part of Ulster is part of the UK. This will probably be difficult.
b) Convince headquarters to rename "United Kingdom" to "Great Britain". In this case no change of attribution of caches would be needed, so it would be easier. However, it would be a bit awkward, as usually top level units ("countries") tend to be actual countries, i.e. souvereign political entities, although there are quite a number of cases where non-sovereign entities get a level 1-listing of their own (e.g. Isle of Man, Guernsey, Jersey etc.). I am not aware, however, of any other case were a level 1-listing comprises territories of two souvereign states (if we do not take into consideration disputed cases like Kosovo).
c) As it will be difficult to change HQ’s policy, PGC could give up it’s policy not to override CO’s attribution when it comes to the top ("country") level. PGC ignores what the CO (wrongly) says when it comes to lower levels, but strangely enough "believes" the CO on the top level. In the Irish case a change of policy would mean that PGC could for its own statistical purposes define Northern Ireland as an additional region of the UK and list all caches there accordingly.