Does leaving home and living alone solve the problem of feeling hatred towards the family and the constant accusations that you are the cause of their problems?

Your family's dislike for you has a cause, and their accusation that you are a source of problems confirms this. Fleeing is not a solution; rather, you must confront the problem and change the behavior for which they dislike you, and act in a way that pleases them in obedience to Allah. The essence of the matter is obedience to Allah, adherence to His religion, and earning His love and pleasure. For if Allah loves a servant, the inhabitants of the heavens and the earth will love him, as indicated by His Almighty saying: ﴿Indeed, those who have believed and done righteous deeds - the Most Merciful will appoint for them affection.﴾