Duchess I don't think I'm being misty-eyed with regards to history (and can talk about all the negatives for women under Gaelic culture as well, from early marriage to the inability to inherit clan lands), but I absolutely acknowledge that individual experiences vary enormously.
Sample an Irish family at random in the 1970s-1990s, and you would definitely find some that were extremely patriarchal where the father's word was law and the women of then family had to run around tending to him. That was the subservient version of womanhood and motherhood that the church actively encouraged.
But surveys and oral evidence of the period suggests that these kind of households were in the minority, and that it was more common for a woman in the family (mother, grandmother) to be dominant or co-dominant with the man. This strong Irish mammy trope occurred everywhere from rural farming families to Moore St traders in Dublin. It appeared across all social classes but may have been less common in middle-to-upper class Dublin amongst the professional establishment. The "Irish mammy" is a facile and fairly recent label for this kind of social power.
Irish women were sometimes rule enforcers if the patriarchy, certainly. The Legion of Mary and similar were full of handmaidens of the church, pushing conformity on everyone (but particularly other women and girls). On the other hand, many others weren't, and there were plenty of Irish women who were known colloquially by their maiden names all their lives, controlled the family finances, were the ones who made major decisions about things like moving house, quietly helped their pregnant daughters on the boat to England rather than hand them over to a laundry ("not a word to your father"), and raised sons who respected women as people enough to marry a strong woman in their turn. It was a limited sort of power in its range, but strong nonetheless.