I agree that the Irish mammy trope isn't anti-patriarchal (I didn't say it was), but it is nonetheless a source of matriarchal power - it is possible for there to be matriarchal counterpoints in a culture that's generally patriarchal. It may be one reason why I and other Irish pp were not socialised into deferring to men and male needs all the time.
My personal theory is that is that it's a carry-over from traditional Gaelic Ireland, where women were never as under-the-thumb as our Anglo-Saxon (and Anglo-Irish) cousins. Up until the 17th century, women in Ireland could legally hold property, instigate divorce against their husbands, qualify as doctors and lawyers, etc. Or at least they could in the majority of the country outside the Pale that maintained Gaelic law and culture. Even after that, during Ascendency rule, the ordinary people tended to keep many of the old traditions along with the Irish language, such as women keeping their own names on marriage, women maintaining control of their own money and anything they owned prior to marriage, women leaving abusive husbands and returning to their families without social censure. It was really the famine, and the disruption to social structure caused by millions dead/emigrated, that pushed these customs into the background along with the Irish language. The Irish mammy is one of the remnants.
There are huge cultural gulfs, both historically and currently, between Britain and Ireland in certain respects. I have lived in both countries and my experiences match the academic analysis. I think it's important not to view the role of women and feminism in Ireland through the lens of a different country - we have different perspectives and priorities, and need different approaches to effect change.