What is the ruling of Islamic law concerning dealing with a son's wife and her children, especially after the father expelled her from the home and refused to support them, taking into consideration the children's previous attempts to care for orphans?

The ill-mannered wife should be advised and warned of Allah's punishment. If this does not work, her custody will be forfeited if there is fear for the children due to her behavior.

It is not obligatory to obey the father in abandoning the financial support of needy children, because their support becomes obligatory upon you, and obeying him in this regard is an act of disobedience.

Inform the father that Islamic law commands whoever swears an oath and then sees something better than it, to expiate for his oath and do what is good. Use gentleness and kindness with him, and make him feel that his grandchildren will be lost if he abandons their care.