What is the solution and how should I deal with a mother who is chaotic, unjust, and merciless, who does not ask about her children, spends her time outside the home neglecting my three siblings, and refuses to care about religious matters? And what are the supplications that can strengthen her faith and make her compassionate towards my siblings?

The mother's right is great, second only to the right of Allah and His Messenger. This is indicated by the Hadith: "Your mother, then your mother, then your mother, then your father." Honoring her is obligatory even if she is a polytheist, as Allah Almighty says: "But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness." Part of honoring the mother is to advise her and warn her against disobedience, such as uncovering her hair and neglecting Hajj and Umrah despite having the ability, but with gentleness and kindness. If she does not respond, seek help from someone who can influence her, while making abundant supplications for her guidance.