What is the solution for dealing with a father who prevents his deceased wife's relatives from seeing their children, and how can one be reassured about the children? Is cutting ties with him considered a sin, and how can one atone for that?

A father does not have the right to deprive his children of their maternal aunt, who is like a mother. He commits a sin by doing so unless there is a legitimate Sharia (definition)-compliant excuse that permits the prohibition, because it involves severing ties of kinship. The sister who asked the question should be patient and try to advise the father, or seek help from someone who can advise him, or seek assistance from the Imam of the mosque to remind him of the seriousness of severing ties of kinship. If the father does not respond, she bears no sin, and she may refer the matter to the judge for custody of her sister's children.