Is it permissible for a mother to buy her son's house and live in it after she swore never to enter it at all, and what is the expiation if it is not permissible?

There is no impediment to her buying the house if its owners permit the sale. If she enters it after purchase, there is no expiation (kaffara) upon her because it has become her home. However, if she enters her son's house where he resides, she must offer expiation for breaking an oath (kaffarat yameen), which is feeding ten poor persons, clothing them, or freeing a slave. For those who cannot afford this, it is fasting for three days. Each poor person should be given half a saa' of the staple food of the land (approximately one and a half kilograms), or it suffices to provide them with lunch or dinner, or to clothe them with garments that are sufficient for prayer. If her son was residing in the house after the purchase and she entered it before he moved out, then the aforementioned expiation is incumbent upon her.