Is the husband obliged to continue maintaining kinship ties with his brother, despite the latter's refusal, and what is the Islamic ruling on the husband and his wife, especially since they prevent kinship ties between the husband and his family, despite their commitment to prayer?

The husband must maintain ties with his brother and beware of severing kinship. Let him initiate the visit to his brother if his brother does not visit him.

He must also warn his brother against disobeying his mother, and seek the help of someone whose advice his brother accepts.

One who severs kinship ties and one who disobeys his parents are committing two major sins and are weak in faith. They are under the will of Allah if they die before repenting.