Let's start by examining the rejection of (4) and (5).
First, notice how you've worded (4): "God intended for children to get leukemia when he created the world and mankind," emphasis added. I might even be willing to cede that (4), as written, may be false specifically from a Christian perspective. However, the Problem arises regardless of when leukemia is introduced to the world: I can simply make a new premise (4'): "God intended for children to get leukemia at some point." And I think this premise is easily understood and easily defended by merely pointing out God's attributes as omnipotent and omniscient: if God does not want some state of affairs to exist in the world, God will not allow that state of affairs. Leukemia is a state of affairs that exists in the world, therefore God intended for it to exist.
Your new premise is based on some other unchecked premises that would be false according to the Bible.
New premises:
1. What God wants is the same as what God allows.
2. That God allows things to happen by virtue of not intervening to change it immediately or prevent it from happening in the first place.
3. That foreknowledge of an action is the same as wanting that action to take place.
Logically premise 1 and 3 cannot be taken for granted as being true. You would need reasons to establish why you think that must be true.
And if those premises aren't true then you can't hold to your original premise that God intends for children to get leukemia.
When you use the phrase "introduced into the world", that requires asking "who introduced leukemia into the world?"
Your premise incorrectly assumes it is God who does that.
12 When Adam sinned, sin entered the world. Adam’s sin brought death, so death spread to everyone, for everyone sinned
-Romans 5
So you see, just as death came into the world through a man, now the resurrection from the dead has begun through another man. 22 Just as everyone dies because we all belong to Adam, everyone who belongs to Christ will be given new life. 23 But there is an order to this resurrection: Christ was raised as the first of the harvest; then all who belong to Christ will be raised when he comes back.
-1 Corinthians 15
We can see it was not God who introduced leukemia into the world.
God created a world without it.
And God restores the world to a state where it will be removed.
With regards to new premise #3:
It is perfectly possible that God could have foreknowledge of what will happen without wanting that to be what does happen.
We see this example replete through the Bible where God warns the people that if they don't repent of their evil ways then disaster will come upon them.
One example of this, because I don't think the fact that this happens repeatedly throughout the Bible is a fact that would be disputed:
“Now listen! Today I am giving you a choice between life and death, between prosperity and disaster. 16 For I command you this day to love the Lord your God and to keep his commands, decrees, and regulations by walking in his ways. If you do this, you will live and multiply, and the Lord your God will bless you and the land you are about to enter and occupy.
“But if your heart turns away and you refuse to listen, and if you are drawn away to serve and worship other gods, 18 then I warn you now that you will certainly be destroyed. You will not live a long, good life in the land you are crossing the Jordan to occupy.
“Today I have given you the choice between life and death, between blessings and curses. Now I call on heaven and earth to witness the choice you make. Oh, that you would choose life, so that you and your descendants might live! 20 You can make this choice by loving the Lord your God, obeying him, and committing yourself firmly to him. This is the key to your life. And if you love and obey the Lord, you will live long in the land the Lord swore to give your ancestors Abraham, Isaac, and Jacob.”
-Deuteronomy 30
We also see elsewhere it is God's desire/will/intention that all people will choose the path of life:
He does not want anyone to be destroyed, but wants everyone to repent.
-2 peter 3
I urge you, first of all, to pray for all people. Ask God to help them; intercede on their behalf, and give thanks for them. 2 Pray this way for kings and all who are in authority so that we can live peaceful and quiet lives marked by godliness and dignity. 3 This is good and pleases God our Savior, 4 who wants everyone to be saved and to understand the truth. 5 For,
There is one God and one Mediator who can reconcile God and humanity—the man Christ Jesus. 6 He gave his life to purchase freedom for everyone.
-1 Timothy 2
With regards to new premise #1:
We know that claim can't be true because we see God giving people a choice between actions that will lead either to life or death.
Therefore, we know God allows for us to make a choice between two options even though He only wants us to make one of the two choices. Because we have already established through Scripture that God wants us to make only one of those two choices.
Thus, it would be accurate to say God allows us to make a choice which he doesn't want to happen.
It would be impossible for us to have the ability to choose which action to take, and have it be a genuine free will choice, if God made it impossible for us to ever choose wrong.
We can therefore state that one of the things God does want is for us to make a free will choice to be with Him.
Logically, doing that would require him to allow us to do something which he does not want: To choose the opposite.
Therefore, it is impossible to say that God wanted leukemia to happen to children when he created the world because we can clearly see that not everything that does happen is what God actually wants to happen.
Given that it is clear that some outcomes are the result of man's individual decisions of free choice, we therefore cannot assume that everything that happens is actually the result of God making the decision for it to happen.
Now, we can pre-empt at least one objection to my defense of (4') right away: consider for instance that somebody argues that God doesn't want broken friendships to exist in the world, but God wants free agency to exist in the world more. It would be reasonable to say then that despite God's omnipotence and omniscience that God could not prevent broken friendships because God cares about preserving free agency. And I would agree.
However, this argument doesn't work for leukemia. Leukemia is not a result of human free agency, and there is nothing stopping God from using God's omnipotence and omniscience from preventing leukemia's existence.
If leukemia exists at any point, it is by God's intention.
Your conclusion is incorrect because it is based on the false premises from above.
This goes back to what I said about the question "who introduced leukemia into the world?'
It was Adam's free will choice through which death and corruption entered into the world:
The Lord God placed the man in the Garden of Eden to tend and watch over it. 16 But the Lord God warned him, “You may freely eat the fruit of every tree in the garden— 17 except the tree of the knowledge of good and evil. If you eat its fruit, you are sure to die.”
-Genesis 2
And to the man he said,
“Since you listened to your wife and ate from the tree
whose fruit I commanded you not to eat,
the ground is cursed because of you.
All your life you will struggle to scratch a living from it.
18 It will grow thorns and thistles for you,
though you will eat of its grains.
19 By the sweat of your brow
will you have food to eat
until you return to the ground
from which you were made.
For you were made from dust,
and to dust you will return.”
-Genesis 3
In contrast, it is through the actions of God that death and corruption will one day be removed from the world.
Then I saw a new heaven and a new earth, for the old heaven and the old earth had disappeared. And the sea was also gone. 2 And I saw the holy city, the new Jerusalem, coming down from God out of heaven like a bride beautifully dressed for her husband.
3 I heard a loud shout from the throne, saying, “Look, God’s home is now among his people! He will live with them, and they will be his people. God himself will be with them. 4 He will wipe every tear from their eyes, and there will be no more death or sorrow or crying or pain. All these things are gone forever.”
5 And the one sitting on the throne said, “Look, I am making everything new!” And then he said to me, “Write this down, for what I tell you is trustworthy and true.” 6 And he also said, “It is finished! I am the Alpha and the Omega—the Beginning and the End. To all who are thirsty I will give freely from the springs of the water of life. 7 All who are victorious will inherit all these blessings, and I will be their God, and they will be my children.
-Revelation 21
“Look! I am creating new heavens and a new earth,
and no one will even think about the old ones anymore.
18 Be glad; rejoice forever in my creation!
And look! I will create Jerusalem as a place of happiness.
Her people will be a source of joy.
19 I will rejoice over Jerusalem
and delight in my people.
And the sound of weeping and crying
will be heard in it no more.
20 “No longer will babies die when only a few days old.
No longer will adults die before they have lived a full life.
No longer will people be considered old at one hundred!
Only the cursed will die that young!
21 In those days people will live in the houses they build
and eat the fruit of their own vineyards.
22 Unlike the past, invaders will not take their houses
and confiscate their vineyards.
For my people will live as long as trees,
and my chosen ones will have time to enjoy their hard-won gains.
23 They will not work in vain,
and their children will not be doomed to misfortune.
For they are people blessed by the Lord,
and their children, too, will be blessed.
24 I will answer them before they even call to me.
While they are still talking about their needs,
I will go ahead and answer their prayers!
25 The wolf and the lamb will feed together.
The lion will eat hay like a cow.
But the snakes will eat dust.
In those days no one will be hurt or destroyed on my holy mountain.
I, the Lord, have spoken!”
-Isaiah 65
So we circle back to where we were before: Your original premises of #4/5 are not true according to the Bible.
That leaves only original premise #3 in dispute. But it's easier to address that issue after we first recognize that #4/5 were obviously not true based on what Scripture says.