1- The cause of their poverty is not their children. It’s other factors like oppression, injustice, unjust economy, and so on.
2- Poverty is a trial. Allah has not promised us not to try us. Yes we have Tawakkul on him and he helps us, but some people Allah has determined that it’s better for their hereafter to stay poor.
3- Yes some of them don’t have proper Tawakkul on Allah. They rely on materialistic means more than Allah. Had they had stronger Tawakkul, their situation would have been better.
4- If someone truly fulfills his religions obligations, has strong Tawakkul on Allah, works hard, is content and not greedy, Allah will truly help him. He many not necessarily become rich or wealthy, but Allah will give him the sustenance that he needs.