Is it permissible to boycott visiting one's brother in his home due to his wife's bad manners, while maintaining communication with him and welcoming him and his daughter when they visit us, and would that be considered severing ties of kinship?

Maintaining kinship ties (silat al-rahim) is subject to custom and has no specific limit defined by religious law. It can be through financial support, visits, or other means. Therefore, not visiting a brother in his home is not considered a severance of kinship ties if the connection is maintained through other means, such as phone calls or gifts. However, if custom dictates visiting, then this obligation is waived if it leads to harm, such as annoyance from the brother's wife, and can be replaced by other means like a phone call.