Chris -- As a new ministerial student, in 1st year college, 16 years old, I remember floating some interpretations of the Trinitarian nature of God. I told my fellow Freshmen (and women) that God was God; his presentation of Himself to the world was as Jesus, and his presentation of Himself to individuals was as the Spirit.
I have not noticeably changed by views, even though my first evaluation was 69 years ago.
Some theological author prided himself, I'm sure, on inventing the application of the word "Trinity" to the God-based processes of communicating his presence to our world. The word caught on, and has been repeated for centuries, causing several kinds of mis-interpretations, rabbit-chasing, theological divisions, etc.
A modern example of the same process is found in the present use of the phrase, "pink slime," for a perfectly harmless addition to ground beef. The resulting up-roar would have been absent, had the media (and/or meat-processers) had a less objectional phrase to describe the innocuous mixture we put into our mouths (and systems) with every bite of a McDonald's, or Burger-King's, or Dairy Queen's, or Hardee's hamburger.
If your class members are bothered by the historical facts concerning the written nature of references to the -- oh, yeah, the Trinity -- remind them of the mysterious nature of much of our knowledge of God's workings . . .
Perhaps it's a good time and place for application of Occam's Razor. (The simplest explanation is usually the right one.)
It is error only, and not truth, that shrinks from inquiry. -- Thomas Paine