Don’t know enough about all of this. Odd that the pope would want England, who left the Catholic Church so their king could get a divorce would want them to take over a Catholic country though.
Good question. I'm just summarizing what O'Connor said in the interview. The short answer is the English invaded Ireland in 1155 AD; whereas the papacy lost direct control in England 1527 AD.
I would suggest her emphasis was one of practical reasoning regarding causes of social ills such as child abuse... rather than very specific history.
Historical Date Background
Christianity came to both Ireland and great britan at the same time, probably somewhere around
250-300 AD. At the time there was just the Church, which was many church communities.
The Roman church slowly became "special" and seen as the head, and eventually "the Pope", which really came to a head in
1054 AD with the East-West Schism. Protestantism would not come into existence until
1517 AD with Martin Luther. As you said, in
1527 AD King Henry VIII put an end to all papal jurisdiction in England with the birth of the Anglican church.
English (Anglo-Norman Invasion of Ireland
With a little research, I did find the concept of Laudabiliter, which some say was a papal bull (papal charter) issued in
1155 AD by Pope Adrian IV who was the only English (Anglo-Norman) pope, that sanctioned the Anglo-Norman invasion of Ireland, with the purpose of enforcing the Gregorian Reforms on the semi-autonomous Christian Church in Ireland. I read the document either never existed or no longer exists; its existence debated. You can checkout the wiki links on this
Anglo-Norman invasion of Ireland, and
Laudabiliter.
The Great Potato Famine, No Pope Connection
The Great Potato Famine was between 1845 to 1852. Generally speaking the British partially employed a laisser-faire response to the famine. Food was allowed to be exported from England during the famine. I couldn't find any negative, or pro-famine response by the Roman Catholic church (RC)... and O'Connor did not say RC was involved in that. Indeed, "Pope Pius IX made a personal contribution of 1,000 Scudi (approximately £213) for famine relief in Ireland and authorized collections in Rome. Most significantly, on 25 March 1847, Pius IX issued the encyclical Praedecessores nostros, which called the whole Catholic world to contribute moneywise and spiritually to Irish relief." (from wiki Great Famine (Ireland))
I did read more recent research indicating the urban Irish Catholics, who attended Mass weekly, were not as helpful as they could have been to the rural Catholics whose attendance was much laxer. Wiki reads there was an attitude that the potato famine was partially caused by poor character of the rural Irish. Much land was acquired by certain folks during the famine, including the RC. I'd suggest no one would argue the famine cause was potato blight; and many people not doing enough to help, and probably some benefitting in an immoral way.
Famine role of Irish church criticised by Catholic paper