All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
Marrying your brother's widow does not make her son (from your brother) your son, but he is a stepson and a nephew; so he has no right to inherit from you – after you die – as if he was your son.
As regards your responsibility towards him, then he is your nephew, he has the right of kinship, so it is an obligation to keep ties with him, and it is forbidden to cut the ties with him. His mother is not allowed to prevent him from keeping ties with his kinship.
Allaah knows best.