How does one honor a father with these characteristics? Is it sufficient to call him by phone despite the expected insults? What should a son do who insulted his father and regrets it, but cannot apologize?

If what was mentioned about the father is true, then he has reached a great level of evil. Accusing his wife of adultery without proof is slander (qadhf), and denying the lineage of his children based solely on suspicion is forbidden (haram). His attempt to sow discord between his daughters and their husbands is an act of instigation (takhbib). Despite this, disobeying him is not permissible; rather, one must honor him and strive for his betterment through supplication and gentle advice, while being careful not to harm him, even if he harms them. Your brother's cursing of his father is a grave mistake, and he must repent, seek forgiveness, and ask for his father's pardon, unless doing so would lead to a greater harm. In that case, he should increase his supplications for him and seek forgiveness on his behalf. Honoring one's father is obligatory, and maintaining ties with him should be done as much as is feasible according to custom, with forbearance, patience, enduring harm, and responding to ill-treatment with kindness.