Is supporting the mother in her demand for her rights from the father, who does not provide for her and their children, considered to be disobedience to the father?

You must support your mother if she is oppressed, and support your father if he is oppressive by preventing him from oppression, because that is a form of supporting him. Your standing with your mother to reclaim her right or preventing your father from oppression is not an act of disobedience to him; rather, it is a form of righteousness towards him and support for him. You should strive to reconcile between them, advise him, and remind him of the sanctity of what he is doing, while maintaining politeness and kindness in your interaction with him.