He vowed that he would not speak to his sisters

If the situation is as mentioned, then this vow was not intended to draw closer to Allah; rather it was the result of an argument and anger, and the purpose behind it was to prevent himself from speaking to his sisters. In brief, this vow comes under the ruling on oaths, so you must offer expiation for breaking an oath (kaffarat yamin), but you do not have to fast. Rather this comes under the rulings on vows which are made during arguments and in anger, the ruling on which is the same as the ruling on oaths.

So you have to offer expiation for breaking an oath, which is feeding ten poor persons, or clothing them, or freeing a slave. This is the expiation for breaking an oath. So if you feed ten poor persons lunch or dinner, or you give each of them half a sa‘ of the local staple food, that will be sufficient; or if you clothe them, that will be sufficient.

Similarly, if someone says: “I am obliged to do Hajj if I speak to So and so,” or he swears that he must do such and such if he speaks to So and so, all that is required in this case is the expiation for breaking an oath, because it was a vow made during an argument or in anger, and the purpose behind it was to prevent himself from doing that thing. End quote.

Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him)

Fatawa Nur ‘ala al-Darb (4/1978).