There are three separate problems with the YouTube video, one, that St Patrick ever taught the trinity using the shamrock; two, that he, or anyone else, ever taught the specific theology of Partialism as defined in the video; and three, that such a theology, if it had been taught, would have been considered a heresy in the 4th century Church.

First, there is no evidence that St Patrick ever used the shamrock as a metaphor for the trinity. We do not have any contemporary evidence as to how he explained the trinity to the Irish. The earliest evidence we have of his theology of the Trinity is from a ninth century hagiography known as the Tripartite Life (Bethu Phátraic) which quotes him as saying: "Our God is the God of all...He hath a Son, coeternal and coequal with Himself; and the Son is not younger than the Father, nor is the Father older than the Son. And the Holy Ghost breatheth in them. And the Father, and the Son, and the Holy Ghost are not divided." Whether this was the theology of Patrick himself, or the ninth century hagiographer is hard to say. Anything earlier than this does not mention St Patrick's understanding of the Trinity, or even that he specifically taught the Trinity to the Irish. The earliest written reference to his use of the Shamrock as a metaphorical aid was in 1726.

Secondly, the video defines partialism as “The father, son, and holy spirit are not distinct persons of the godhead but are different parts of god, each composing one third of the divine”. As far as I know however this is not a historically defined Christian heresy, either under the name of Partialism, or as described under any other name.

Thirdly, I don’t think that Partialism, as defined by the video, would have been considered a heresy at the time. In fact Tertullian's work 'Against Praxeas' (Adversus Praxeam) 155 – 240 AD actually uses a very similar plant metaphor for the Trinity as the Shamrock. In chapter 8 he compares the three persons of the Trinity to the root, trunk, and fruit of a tree.

Over a century later at a Synod in Alexandria in 362 CE, Athanasius and his followers declared that it was acceptable to refer to the Father, Son, and Holy Spirit as "of one substance" as long as this was not understood as obliterating the distinction among the three, and that it was also legitimate to speak of "three substances" as long as this was not understood as if there were three gods." (from The Story of Christianity, Revised Edition, by Justo Gonzalez. Chapter 17, "The Arian Controversy and the Council of Nicea.")