Is it permissible for the paternal uncle and his wife to have custody of their deceased brother's children, given that their mother has married someone else and the children's paternal grandparents have relinquished custody?

The person with the most right to the custody of the children here is their maternal grandmother, unless she is incapacitated or relinquishes her right, in which case the maternal aunt takes precedence. Distinguishing children are given a choice between the grandmother and the closest male relative (the father in this case), and they will reside with whomever they choose. If the grandmother is unable to provide custody, then the maternal aunt takes precedence. Custody can be given to the mother if she is fit for custody and not preoccupied by her husband's obligations.