The idea that God kills by lawful authority only makes sense if God is doing the killing. When God tells the Hebrews to enter Canaan and kill everything that lives, including women and children, God is commanding them to break the very commandment God gave them, which is absurd and morally repugnant.
My suggestion: Let Christ be the primary lens through which you understand God and through which you interpret the OT. Discard any notion of God that does not align with Christ and the love of God he revealed. If you fail to do that, you will hold inconsistent notions of God and accept ad hoc arguments that try to defend the indefensible. First and foremost, the scriptures are a witness to Christ, for which they are sufficient with and only with the combined witness of the Holy Spirit. Once the Spirit dwells in you, then Christ becomes the proper interpretive key. Without that, the scriptures can be used to justify all kinds of atrocities, which history has shown to happen over and over again.
ETA: Augustine made a similar point in saying if your interpretation doesn't fall within the bounds of the dual commandment to love God and neighbor, then get a better interpretation that does. Admittedly, Augustine didn't always adhere to his own guidance, but it was still good guidance.
Early interpreters understood some of the problems in reconciling God as portrayed in the OT and God as revealed in Christ, which was one reason they favored allegorical interpretations of the OT and cautioned against sticking to a literal reading. Origen has a very helpful discussion on this very problem where he points out various inconsistencies in the narratives and even the laws! These same issues led folks like Marcion to claim that the God of the OT was not the Father of Jesus. Origen, by contrast, brought the two testaments together not by ad hoc arguments trying to defend the indefensible but by reasonable moral insight.
"By all which it is established, that the God of the law and the God of the gospels is one and the same, a just and good God, and that he confers benefits justly, and punishes with kindness; since neither goodness without justice, nor justice without goodness, can display the dignity of the divine nature." De Principiis II.5.3
Of course, Origen believed in apokatastasis, which makes good moral sense, too.