One thing I would say to your father is why would he assume that he can get his mind wrapped around the Trinity? If God is infinite and eternal, how could our finite and mortal minds wrap around Him? So the fact he doesn’t fully understand it is good, no one who believes in the Trinity does.
But the easiest way it was explained to me was: In the One Being/Nature/Substance of God/The Divine are three co-equal and co-eternal Persons, namely, Father, Son, and Holy Spirit. These Three Persons are not eachother, but seperate in their Personhood. Emphasizing the distinction between person and being is vital. If one doesn’t understand the distinction then the Trinity will be missed. An example of the distinction would be: A human is a being and a person, but a rock is not a person but has being/nature.
You misspoke when you said:
God is not one person, but three Persons in One Being. Some will think how is that possible? Since God is outside of time and the material realm, why would we question how God can exist in this way? If God exists out of dimensions, then He is a hyper-dimensional being meaning He can exist in ways that are different than us. To assume God must exist as one person in one being is a fallacy. God has revealed in Scripture that He is One, but that He exists as three co-equal and co-eternal Persons.
Hope that helps