Was it correct to resort to the security authorities against a brother who was disobedient to his parents, did not pray, and was violent with beating and cursing, after more than 30 years of patience and endurance?

We advise patience and endurance, and to counsel your brother, even through indirect means. There is no harm in reporting him to the official authorities since he is an aggressor and a sinner. Abandoning prayer and disobeying parents are among the greatest major sins. If communicating with your brother causes you distress or sin, then there is no sin in ceasing communication with him.