How can one honor a father who verbally abuses and mistreats the mother, given that peaceful attempts at reconciliation have failed, and is it permissible to shun him for a day?

Anger and nervousness are gateways to evil. The best way to honor one's father is to be patient with him and supplicate for his righteousness, while being careful not to harm him. If it is possible for righteous people to advise him, then do so. It is not permissible for a child to abandon his father. Some opinions may permit it for a legitimate benefit, but usually there is no benefit in that.