How can one honor estranged and distant parents, deal with one parent's jealousy when visiting the other, or with one parent's harshness and favoritism towards a sibling, while maintaining God's pleasure and avoiding undutifulness towards parents, especially when there are complex family and financial disputes?

The father's negligence in providing for his family and the mother's differential treatment are both wrong. Nevertheless, one must still be dutiful to one's parents, for there is no obedience to a creature in disobedience to the Creator. You should not boycott your father while pleasing your mother. It is also possible to find a way to meet your father without angering your mother. As for marriage, you can involve your mother, ask for her help, show keenness to gain her approval, and supplicate frequently.