What is the ruling on a mother favoring her own family and her sisters' children over her own children, and what should the children do in this situation?

The natural state is for a mother to be compassionate towards her children, and what you describe about your mother is unusual. We advise you to be patient with her, for patience has good consequences. Repel evil with good, as Allah Almighty commanded in Surah Fussilat, verse 34. As Ibn Kathir said, showing kindness to one who has wronged you leads to affection. You should also supplicate for her guidance, for supplication works wonders. Allah has commanded supplication and promised to answer it in Surah Ghafir, verse 60. Continue to be dutiful to her, as it is an obligation upon you, and beware of disobeying her. Perhaps Allah will open doors of good for you because of this dutifulness. Increase your supplications and piety, for through them you can obtain a job or a righteous spouse, as stated in Surah At-Talaq, verses 2 and 3. Strive to find a righteous husband, for he might be a cause for your happiness.