Is what the father does permissible, in terms of neglecting his first wife and his adult children in their financial responsibilities, and must the son continue to spend on his mother and her travel expenses despite his straitened circumstances and debts?

It is not permissible for a man who has multiple wives to differentiate between them in terms of overnight stays and financial support, except with their mutual consent. Otherwise, he will come on the Day of Resurrection with one side of his body drooping. The wife may gently and kindly advise her husband's father that what he is doing is not permissible unless the wronged wife consents. As for the husband and his mother, honoring one's parents is one of the greatest acts of piety. It is not permissible to prevent the husband from honoring his mother unless he is giving her from his wife's private money, or depriving his wife of her obligatory financial support to give it to his mother for her superfluous needs. A husband taking his mother out for a stroll is considered an act of honoring her, and he is permitted to incur debt for that purpose.