All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
If the aim behind making the vow is to urge oneself to do something or abstain from doing something, then this is what the scholars refer to as a vow of lajaj, i.e. a vow of anger. Muslim scholars held different opinions regarding what a person who makes such a vow is required to do if he fails to deliver on it. There are three opinions in this regard:
Firstly, it is obligatory on the person in such a case to offer expiation like for breaking an oath. The Prophet, sallallaahu ‘alayhi wa sallam, said: "The expiation for (breaching) a vow is the same as that of (breaching) an oath)." [Muslim] This is so because the person, in this case, makes a vow just to urge himself to do something or abstain from doing something but does not intend to do an act that draws him closer to Allaah, the Exalted. This is one of the opinions of Ash-Shaafi‘i, and it is the adopted opinion of the Hanbali scholars.
Secondly, he is obliged to fulfill the vow that he made. This is the opinion of the Maaliki scholars, although some of them adopted the first opinion.
Thirdly, he has the choice either to offer expiation like that of breaking an oath or to fulfill his vow. This is because this kind of vow is similar to an oath in terms of urging oneself to do something or abstain from doing something. In the meantime, it is similar to a vow in terms of committing oneself to do a certain act that draws one closer to Allaah, the Exalted. Imaam An-Nawawi who belongs to the Shaafi‘i school of Fiqh considered this last opinion preponderant. We believe that this is likely to be the preponderant opinion, Allaah Willing.
Having said that, we would like to inform you, dear questioner, that the vow that you made is considered a vow of lajaj, but it is also a vow to do an act of obedience that is conditional on committing a sin. You have to do two things:
1) You should break that vow and maintain your kinship ties with your sister.
2) You should offer expiation like for breaking an oath or deliver on your vow and fast a whole month successively. You have the choice to do one of these two things.
We have previously underlined the expiation for breaking an oath and how it should be paid in Fataawa 204 and 2053.
Allaah Knows best.