Since Islam is a proponent of institution of family. In order to maintain any institution, there needs to be a head of that institute with rights and responsibilities of each party laid down explicitly. This is exactly what Islam did, by making Husband solely responsible for the Kids brought to this world, irrespective of the fact that couple is divorced or living separately. In addition to that, Islam recognizes sacrifices made by a wife-cum-mother, therefore it also puts responsibility on the Husband to give maintenance to the wife in case of divorce and to not take back any property, dowry already given to the wife. Ideally, every God fearing Muslim should follow these instructions of Allah, and if not, it is responsibility of the state to enforce these injunctions by force and give wife her due right.
Sadly, no such state exists which is implementing these Islamic injunctions in their true letter and spirit. Mostly, it’s the fiqh which came into existence in later times and took the form of a proper source of religion (without any basis). That fiqh of earlier times practically failed to rise above the societal influences, customs and norms of that era which was a male dominated society and the same was reflected in the fiqh of that time. The same fiqh got carried forward in later times and hence no reconstruction of religious thought took place after a certain time. That is the main reason, Muslim women living in Islamic countries feel exploited by the law itself which was made in the name of religion.
Nevertheless, true Muslim believers (men & women alike), like other aspects of life, shouldn’t give up on these hardships and must face these challenges like the ones they’re facing in other domains of life. God has given glad tidings to those believers, who understand this test and participate in it with all courage and high ethical values. When God says He is with Sabireen (Patient ones); the word ‘sabr’ in this context means ‘to stick to the right path with all patience and courage and to accept whatever test you’ve been put through by submitting complete trust in Allah’.
Insha Allah the reward will be multiple folds with the level of hardship a single parent (mother) has to go through, provided that she exhibits ‘Sabr’ in this life in exchange for an eternal kingdom.