What is the just legal ruling in the case of a brother demanding payment of half the rent for another, more expensive apartment, in violation of the prior agreement that the rent for the new apartment would not exceed one hundred pounds, knowing that the brother is deaf and his wife is the cause of the problem?

The perpetual lease contract is Islamically invalid. Therefore, you and your brother have no right to inherit the usufruct of the apartment, and it must be handed over to its owners. The agreement between you and your brother to compensate him in exchange for him vacating the apartment is not valid, and you are not obligated to fulfill what you promised him. You must vacate the apartment and hand it over to its owners unconditionally, and seek their forgiveness for the past unlawful usufruct of it.