1) God does not compel us to sin. We choose to sin. But he allowed us to sin by giving us free will. So what is meant by God willing for it means he has willed to give you the means to sin, not that he compelled you to sin. Allah willed for you to have free will and choose to sin or not. So when you sin, you don’t overpower God. You don’t do so without His permission. He allowed you to do it (to try you). That’s how we can understand this concept in simple terms.
2- When a child is killed unjustly, God condemns it and those who killed the child, but God allowed it because:
-He is trying people and he will hold them accountable
-He will compensate the child and take him to heaven
So there is wisdom in allowing it.
3- Imam Hussain (a) did not cause his family to suffer. The enemies caused it. Yes, Imam Hussain (a) allowed for it by taking them with him because it’s a sacrifice he had to make. There was wisdom in doing so.