2386 It can happen that one of the spouses is the innocent victim of a divorce decreed by civil law; this spouse therefore has not contravened the moral law. There is a considerable difference between a spouse who has sincerely tried to be faithful to the sacrament of marriage and is unjustly abandoned, and one who through his own grave fault destroys a canonically valid marriage.
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So, in a domestic violence situation where the wife, in order to preserve not only her life, but the lives of any children involved, files for divorce in a civil court, does not contravene the moral law? If she has honestly tried to make the best of things, to keep her vows and diligently attempt to keep the marriage together, but fails anyway, has she committed a mortal sin? And what if, after the divorce is finalized, she meets someone else and marries? Is she living in sin?
In my humble opinion and according to what I BELIEVE the chuch says about this, in the situation you describe, the woman would NOT be committing a mortal sin to divorce the husband, especially if she has pursued every avenue of counciling etc. Indeed, it is her duty to protect her children. As to remarriage, if she waits the appropriate time (I believe one must wait at least a year after the civil divorce), then seeks an anullment from the church and marries the new spouse in the church, then NO she is not living in sin.
However, if she marries without first obtaining the anullment, or if she fails to obtain an anullment for some reason and marries anyway (and it would have to be outside the church), then yes, she would be living in a state of sin, as she would, in the eyes of God and Church, still be considered married to the first husband.
Of course one must understand that in the anullment process, the church looks to establish whether there was really a valid marriage in the first place. Nothing breaks the bond of a valid marriage, not even abuse or adultery. The abused spouse certainly can separate from her abuser and seek a civil divorce without sinning.
As far as the anullment process, sometimes the church can through interviews with witnesses, doctors, the two people involved etc, determine that there was never a valid marriage to begin with. Perhaps the abusive spouse had a history of abusive relationships. The church might see this as an indication that he never intended to enter into a marriage as Christ intended. Or perhaps the tribunal might determine that you were somehow unduly pressured either by your husband or by your parents to enter into a marriage. That would render it invalid.
As I said, if you can get the anullment, then you may enter into another marriage, if not, then you must stay celibate for the rest of your life, knowing that you have preserved your life and that of your children.