You are correct; God loves his children, not everybody.
Otherwise he would be lying when he says he "hates all workers of iniquity" in an early Psalm...not sure which one exactly, but below 10.
However, God is still truly love even when he hates evildoers, as Scripture says in the NT that "God is love"....it is a paradox, but Scripture is full of such tensions for a reason. God is not a being we can fully understand.
God's word is not full of paradoxes. That sounds like Cornelius Van Til. God does not hate and love someone at the same time. That makes God the author of confusion and we know that is false. Further, if God loved the reprobate, He would have sent His son for them. Love is not an emotion, it's an action, and God is actively working against those He had no love for.