"You are re-defining God as being only the Holy Trinity"
The church proclaims, "God in three persons". My post affirms that and that Jesus is fully God in the undivided divine essence, however there is a certain order in subsistence and operation of the three persons in the divine Being as well as certain personal attributes that distinguish the three persons of the trinity. The Father is neither begotten by, nor proceeds from any other person; the Son is eternally begotten of the Father, and the Holy Spirit proceeds from the Father and the Son from eternity. There is a subordination in respect to order and relationship, a logical order of derivation, but not to any priority of time or essential dignity. The divine essence is not an independent existence alongside the three persons.
Your filioque is repeating the tradition of men. Double procession is not from all eternity.