Respectfully, one question I've always had about the Holy Trinity is, why did God use anger, war, and violence to solve problems in the OT and then use love, compassion, and healing in the NT to solve problems?
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No, you are quite mistaken. Eg .......
ACTS.5: =
7 Now it was about three hours later when his wife came in, not knowing what had happened. 8 And Peter answered her, “Tell me whether you sold the land for so much?”
She said, “Yes, for so much.”
9 Then Peter said to her, “How is it that you have agreed together to test the Spirit of the Lord? Look, the feet of those who have buried your husband
are at the door, and they will carry you out.” 10 Then immediately she fell down at his feet and breathed her last. And the young men came in and found her dead, and carrying
her out, buried
her by her husband. 11 So great fear came upon all the church and upon all who heard these things.
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Do you know what God did to the Jews who had rejected Jesus as the Christ/Messiah and proceeded to 'kill' Him on the Cross in 33AD.? (cf; LUKE.21:20, MATTHEW.24:15-16 & 24, ROMANS.12:19-21)
... The stubborn Jews and Pharisees were massacred and their Holy Temple of God in Jerusalem was destroyed by the Roman Army in 70AD.
Jesus Christ came down to earth(ie from heaven) on a mission to save people from hell.(cf; MATTHEW.5:17-48) He had to submit to evildoers/sinners and be killed or sacrificed, in order to fulfill His mission or the will of the Father.
... So, Jesus did not resist or curse/punish/harm the Jewish persecutors, accusers and murderers, eg MATT.26:53.
God's/Jesus's love, compassion and healing did not change from the OT to the NT. Similarly, Man's inborn propensity for sinfulness/evilness/satanism did not change from the OT to the NT. Only the way to heaven did change from the OT to the NT.(cf: JOHN.14:1-6, LUKE.16:19-31)
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P S - The mission of Moses in 1500BC was to 'save' the Jews from Egyptian(= symbolic of Satan) slavery and lay down God's Law for the Jews(EXODUS.20, DEUT.28), in order to curb Man's inborn propensity for committing sins = a peaceful, orderly and prosperous nation or kingdom = Israel/Judah
... Alas, the Jews failed to keep Moses Law faithfully and God cursed/punished them into foreign rule/colonization in 500BC, ie back to 'Egyptian slavery'.