What should a young man do who is prevented by his family from going to the mosque, and is it better for him to stay with his brother who helps him in matters of his religion?

If the parents prevent (one) from congregational prayer or learning the obligatory knowledge in the mosque, then their obedience is not binding. The Muslim must endure what he faces for the sake of his religion. If the elder brother helps in obeying Allah, while the mother prevents (one) from praying in the mosque and orders (one) to drink alcohol, then the son should reside with his brother and not abandon showing kindness to his mother.