What is the ruling of Islamic law regarding a husband who is unable to be just between his two wives, and faces difficulties in providing for the children of his second wife whose fathers do not provide for them, and is he obligated to respond to the requests of the second wife who does not wish to move in to live with him permanently?

The husband must treat his wives equally in terms of maintenance, clothing, and housing, according to their needs. He may, however, give more than that to one of them. The husband is not obliged to provide for the children of his wife from another man; rather, their maintenance is the responsibility of their father. The stepfather will be rewarded if he spends on them voluntarily, and he may claim reimbursement from the father for the maintenance if he spent with the intention of doing so. Fulfilling a promise is desirable, and you should fulfill what you promised your wife. Taking her to her family is a good deed for which you will be rewarded. The custody of children transfers to the one who is more deserving if the mother remarries.