What is the ruling on a grandmother going to a place which she swore by expiation and for 12 months not to enter, after the death of her husband who used to live in that place? And is expiation binding upon her if she goes, and what is it?

If your grandmother's oath does not involve one of Allah's names or attributes, such as her saying: "By the kaffarah and twelve months," then this utterance is not considered a valid legal oath, because it does not include the mention of Allah. An oath is only valid when sworn by Allah Almighty or by one of His attributes, as stated in the Hadith: "Whoever takes an oath, let him swear by Allah or remain silent." Therefore, there is no blame upon your grandmother for going to the aforementioned place, and no expiation is required of her.