As Todd pointed out, they are fashion, or "trade", tartans. Neither of the "National", nor any of the "County" tartans has any standing in Ireland itself. Wear whatever suits your fancy.

I just had a laugh at what your mother said (reminds me of my grandmother)...I know a lot of O'Briens, O'Connells and O'Reillys who'd disagree with her.
I'd be one of the O'Briens who would question the remark.