A Catholic wife in such a position should not concede that her husband has any power to end a presumptively sacramental marriage. She cannot prevent him from obtaining a civil divorce – and may herself have to concede to obtaining a civil divorce to legally protect her children and herself from a man who has abandoned them – but she should realize that the civil divorce is the ecclesial equivalent of a legal separation and is not, in and of itself, a dissolution of the marriage.
That being the case, an annulment would indeed be necessary to obtain before even starting a romantic relationship with anyone else, much less considering marriage, during the lifetime of her presumptive husband. All that an annulment does is to determine whether or not the marriage was sacramental from the beginning, and so abandonment does not necessarily mean that the marriage was invalid from the beginning. Until an annulment is granted, the Catholic wife must presume herself to be married and live a life of chastity appropriate to a married woman (i.e., no romantic relationship with anyone but her husband). If an annulment is denied, she must continue to consider herself married while her presumptive husband lives.
I know this sounds hard, but marriage is not an ecclesially-sanctioned boyfriend/girlfriend relationship in which an abandoned spouse may find someone else with whom to “hook up” in the event of abandonment. Marriage is a sacrament that forms the couple in sanctity, and the abandoned spouse still open to receiving the graces of the sacrament of matrimony can still be formed in sanctity by those graces and can pray and sacrifice for the conversion of the “fallen-away” spouse. All too often, marriage is not a bouquet of roses but a crown of thorns, leading the couple not to happily-ever-afters but to passion, death, and resurrection to eternal glory.
