Is the husband considered sinful for not being able to provide for his children from his divorced wife, especially after he requested their custody and she refused, and is she considered sinful for preventing him from seeing and speaking with them?

If the father is unable to provide for his children, he is not sinful. The mother does not have the right to prevent him from seeing his children, and by doing so, she is sinful and severs ties of kinship. The jurists have stipulated that the custodian should not prevent the other parent from seeing the child. Scholars have differed on the age at which custody ends. The majority of jurists hold that custody goes to the father if the parents are in distant countries. The Sharia (definition) court is the one that settles custody disputes.