Good graphic. It was always the position of the Orthodox Church that Catholic teaching on Trinity made the Holy Ghost "lesser" or "secondary" which your graphic aptly reveals. The orthodox graphic shows that the Father is the first cause and source without confusion or any need to explain further. The Catholic graphic shows what most Catholics believe but deny -- that the Father begts the Son and the Two then begt the Ghost.
Off to presanctified this evening..you are in my prayers.
Why "beget"? The Catholics do not insist on blurring the distinction between proceeding and begetting and my graphic says "proceeds". So does the Latin Creed.
The graphic says nothing about persons being secondary. You wish to see it as dropping the Holy Ghost down. I see it as elevating the Son, in comparison with the Orthodox. Either view is incorrect because it sees the "up" and the "down" of the picture are meaningful. In fact only the relations are meaningful.
The Catholic dogma is that all three persons are consubstantial. There are no lesser persons.