With regard to your question of a woman living with a physically and verbally abusive husband, the Church permits separation (with the marriage bond remaining intact) where there is “grave mental or physical danger to the other spouse or to the offspring.” (CIC, Canon 1153). Have listed the applicable sections from the Catechism and Canon Law:
Catechism of the Catholic Church
2383 The separation of spouses while maintaining the marriage bond can be legitimate in certain cases provided for by canon law.176 If civil divorce remains the only possible way of ensuring certain legal rights, the care of the children, or the protection of inheritance, it can be tolerated and does not constitute a moral offense.
176 Cf. ⇒ CIC, cann. 1151-1155.
Code of Canon Law
SEPARATION WITH THE BOND REMAINING
Can. 1151 Spouses have the duty and right to preserve conjugal living unless a legitimate cause excuses them.
Can. 1152 §1. Although it is earnestly recommended that a spouse, moved by Christian charity and concerned for the good of the family, not refuse forgiveness to an adulterous partner and not disrupt conjugal life, nevertheless, if the spouse did not condone the fault of the other expressly or tacitly, the spouse has the right to sever conjugal living unless the spouse consented to the adultery, gave cause for it, or also committed adultery.
§2. Tacit condonation exists if the innocent spouse has had marital relations voluntarily with the other spouse after having become certain of the adultery. It is presumed, moreover, if the spouse observed conjugal living for six months and did not make recourse to the ecclesiastical or civil authority.
§3. If the innocent spouse has severed conjugal living voluntarily, the spouse is to introduce a cause for separation within six months to the competent ecclesiastical authority which, after having investigated all the circumstances, is to consider carefully whether the innocent spouse can be moved to forgive the fault and not to prolong the separation permanently.
Can. 1153 §1. If either of the spouses causes grave mental or physical danger to the other spouse or to the offspring or otherwise renders common life too difficult, that spouse gives the other a legitimate cause for leaving, either by decree of the local ordinary or even on his or her own authority if there is danger in delay.
§2. In all cases, when the cause for the separation ceases, conjugal living must be restored unless ecclesiastical authority has established otherwise.
Can. 1154 After the separation of the spouses has taken place, the adequate support and education of the children must always be suitably provided.
Can. 1155 The innocent spouse laudably can readmit the other spouse to conjugal life; in this case the innocent spouse renounces the right to separate.
This article from Catholic Answers goes into more detail: