Many have thought this through. It’s a logical difficulty in the study of the problem of evil (theodicy) within monotheism. Different religions handle it differently.
Your metaphor of God as a parent means that you accept that God is either not all-powerful or that he thought it wise to let the Shoah happen, which makes him not especially benevolent. Without either one of those attributes (glory, goodness) is he really God? A Catholic would make reference to the Devil and would not worry so much about the charge of polytheism, even though one could level the charge that the Devil verges on being an evil god, as in Greek and Roman mythology. We aren’t polytheists but we are not as worried about the question as Jews or evangelical Protestants.
To me, people like Elie Weisel who express anger at God over the Shoah are being logically strict monotheists. My personal choice is to relax my logic on the question of whether God is responsible for horrible things happening. Catholic theology allows me to do this.
But to return to the original topic of the thread. I went to Catholic school and spent 3 years in div school, and I never encountered a justification for the Trinity based in Hebrew scripture. Christology was not my area of specialty, but you should be aware that the argument you are attacking is not the one commonly made, for Catholics at least.