Am I obligated to visit my brother who used to beat me and my mother, especially after he was afflicted with a mental illness?

Maintaining kinship ties is one of the obligations and duties of Islam. Allah has warned against severing them, saying: "So would you, perhaps, if you turned away, cause corruption on earth and sever your ties of kinship? Those are the ones whom Allah has cursed, so He made them deaf and blinded their vision." And the Messenger of Allah, peace and blessings be upon him, said: "A severer (of kinship ties) will not enter Paradise." The questioner should take the initiative to connect with his brother, visit him, forgive him, and pardon him. Allah rewards those who pardon people, as He Almighty said: "And hasten to forgiveness from your Lord and a Garden whose width is the heavens and the earth, prepared for the righteous Who spend [in the cause of Allah] during ease and hardship and who restrain anger and who pardon the people - and Allah loves the doers of good"; and "So whoever pardons and makes reconciliation - his reward is due from Allah"; and "And let them pardon and overlook. Would you not like that Allah should forgive you?"