Yes the Irish Twins discuss with St Patrick the beliefs rejected by the church catholic.
In Bible college we were required to write a clear definition of the Trinity in our own words.
Mine read as follows:
"We believe in the one true God beside Whom is no other. The one true God exists eternally as three distinct persons - each one of which has eternally possessed all of the attributes necessary that He might be correctly referred to as the one true God."
That brings in all of the things necessary to say in order to escape the charges leveled by the Irish Twins. It has served me for more than a half century and I have quoted it or something like it in order to correct the various "heretical" formulations I have heard from fellow Trinitarians.
I still do correct them even as I, myself, have broadened my horizons in that regard.
One thing has really struck me as I have studied the subject in the last 20 years or so and listened to numerous debates on the subject. That is the quickness of Trinitarians to condemn to Hell those who take other views. This - in spite of the fact that a full 95 or more percent of their own brothers and sisters and even their elders and pastors couldn't provide a non-heretical definition of the Trinity to save their souls.
It's almost impossible to listen to a debate between a Trinitarian and a Oneness proponent wherein someone doesn't resort to creating straw men out of the supposed beliefs of their opponent.
In short - after approaching the subject with studied fairness - I have come to the conclusion that both the Oneness and Trinitarian models as rightly defined have something to recommend them.
** I am quick point out here that I can't let many other conflicting views about the nature of God (such as Arienism) off the hook so easily.