She swore to leave her husband – what is the ruling on that?

Praise be to Allah.

The oath to leave your husband does not affect the marital relationship between you, because separation and divorce are in the husband’s hands, not the wife’s. If a woman clearly states the words of divorce, that does not have any effect. 

Each of you should treat the other kindly, and avoid speaking of separation altogether, because the husband may be provoked by his wife’s saying that, and then he may issue a divorce. This is what the shaytaan wants and strives for, so as to destroy the family and destroy the home. Also, if one spouse feels that he does not want the other to stay with him, this is offensive and may cause trouble, so that must be avoided as much as possible.
With regard to your swearing to separate from your husband, it is better not to do that, because divorce is hated by Allaah. It is better for you to stay with your husband, and you have to offer kafaarat yameen (expiation for breaking an oath). 

The Prophet (peace and blessings of Allaah be upon him) said: “Whoever swears an oath then sees that something else is better than it, let him do that which is better, and offer expiation for his oath.” Narrated by Muslim (1650). 

The expiation for breaking an oath is that which is mentioned in the verse in which Allaah says (interpretation of the meaning): 

“Allaah will not punish you for what is unintentional in your oaths, but He will punish you for your deliberate oaths; for its expiation (a deliberate oath) feed ten Masaakeen (poor persons), on a scale of the average of that with which you feed your own families, or clothe them or manumit a slave. But whosoever cannot afford (that), then he should fast for three days. That is the expiation for the oaths when you have sworn. And protect your oaths (i.e. do not swear much). Thus Allaah makes clear to you His Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) that you may be grateful”
[al-Maa’idah 5:89]

See also the answer to question no. 45676. 

We ask Allaah to reconcile between you and your husband and to bring you together in goodness and guidance. 

And Allaah knows best.