Using the word allow instead of create implies that they actually have a choice to be allowed. According to your doctrine thus is not the case. According to your doctrine we do not have any choices that God hasn't already decided for us before we were born.I agree with this definition. I prefer the simpler definition: "a volition to favor".
Preample1: Definition of "hate": "A volition to disfavor".
Strictly speaking, wrath/hate is not an attribute of God’s nature, but is his “holy justice against sin”. Joel Beeke Reformed Systematic Theology
Preample2: “A love of holiness cannot be without a hatred of everything that is contrary to it. As God necessarily loves himself, so he must necessarily hate everything that is against himself; if he did not love his image, and loathe what is against his image, he would loathe himself, he would be an enemy to his own nature.
Answer: No, God does not take willful delight (volition to favor) in the children of Satan. He Hates (volition to disfavor) said children.
Leviticus 20:23; Psalm 2:4-9; Psalm 11:4-5,6; Psalm 11:5; Psalm 58:10a; Proverbs 3:32a; Proverbs 6:16–19; Nahum 1:2; Hosea 9:15; Malachi 1:3-4; John 3:36; Romans 9:13; Romans 9:22; 1 Corinthians 16:22; Revelation 14:10, 11; Revelation 18:20; Psalm 5:4; Psalm 7:11; Psalm 11:5-7; Habakkuk 1:13
Aside: I don't accept the terminology in the premise ... specifically the wording "create them to do evil". I prefer the word "allowed" instead of "created".
Answer: No. Same logic as previous answer. God is Holy and just. He cannot love (volition to favor) who He hates (volition to disfavor).
And why would God (in your doctrine) hate sin when he was the one who decided that Adam would sin before creating Adam. According to your doctrine your God is directly responsible for the existence of sin and evil. And your God hates the children of satan, though they are only children of Satan because your God has decided that for them. Your God creates people for the sole purpose of hating them and having them spread more evil. That is why your God is an evil God.
Thankfully your doctrine is wrong.