Is the sister obligated to fulfill her previous promise to waive her share of her mother's inheritance, considering that she swore to her brother's wife to prevent her from informing her mother of her son's death, and is she sinful for spending part of the amount she was supposed to waive?

Fulfilling a promise is considered mustahabb (recommended) by the majority of scholars, while breaking it is makrooh tanzeehan (disliked in a mild sense, not leading to sin). Therefore, there is no sin upon the sister for what occurred, and there is no blame on her regarding the money she spent from her share of her mother's inheritance. She must, however, offer expiation for her oath.