Is it permissible in Sharia for a brother to sever ties with his family and leave the home with his wife and child due to his wife's jealousy of the family's affection for the child, and are the brother and his wife considered blameworthy for this abandonment, which has lasted for a year and deprived the family of seeing the child?

This brother's abandonment of his parents and siblings and his severing of ties with them is a grave mistake and a great sin. He must repent and reconnect. Your love for the child and your care for him do not justify this estrangement.

Perhaps the reason for the abandonment is your excessive love for the child, which made his mother feel jealous. The problem can be solved by apologizing and not exaggerating in playing with the child or taking him from his mother, and by involving some respected community figures. His wife shares in the sin if she was the cause.