As to invasions of Ireland, It was Henry II who landed a force at Wexford in 1171. The threat of the "Danes" was from an earlier period; The Battle of Clontarf for example was in 1014. And the first Norse settlements in Ireland were around 853.
http://www.waterfordcountymuseum.org/ex ... 6/?lang=en
http://www.wesleyjohnston.com/users/ire ... tml#church
Also, there are references in the Anglo Saxon Chronicle to the Pope in Rome sending the Pallium to various Bishops or the Bishop traveling to Rome to receive it or the Pope sending someone to Ireland or England:
"A.D. 430. This year Patricius was sent from Pope Celestinus to
preach baptism to the Scots." (N.B. That is Patrick going to Ireland, not Scotland btw)
A.D. 596. This year Pope Gregory sent Augustine to Britain with
very many monks, to preach the word of God to the English people.
A.D. 601. This year Pope Gregory sent the pall to Archbishop
Augustine in Britain, with very many learned doctors to assist
him; and Bishop Paulinus converted Edwin, king of the
Northumbrians, to baptism.
A.D. 667. This year Oswy and Egbert sent Wighard, a priest, to
Rome, that he might be consecrated there Archbishop of
Canterbury; but he died as soon as he came thither.
A.D. 1022. This year went King Knute out with his ships to the
Isle of Wight. And Bishop Ethelnoth went to Rome; where he was
received with much honour by Benedict the magnificent pope, who
with his own hand placed the pall upon him, and with great pomp
consecrated him archbishop, and blessed him, on the nones of
October. The archbishop on the self-same day with the same pall
performed mass, as the pope directed him, after which he was
magnificently entertained by the pope himself; and afterwards
with a full blessing proceeded homewards.
A.D. 1047 ....And in this same year was the great synod at Rome, and King Edward sent thither Bishop Heroman and Bishop Aldred; and they came thither on Easter eve.
And there are others. The connections and influences in western Europe are not simple but quite intertwined.
Ebor