Does my not responding to my father and refusing to see his new wife constitute disobedience, especially since I want to spare my mother, who has no one but us, knowing that my father divorced my mother to marry someone he met online and who is much younger than him?

A father is responsible for caring for his children and providing for their needs. They are a trust for which he will be questioned on the Day of Judgment. The son must honor his father, visit him, maintain ties with him, and obey him in what is good. It is not permissible for him to abandon or disrespect him, even if the father abandons him or treats him poorly. It is the father's right to marry a second wife, and the children should not resent her if she is righteous; rather, they should preserve her rights. The son should strive to reconcile his parents or mediate between them, by asking the mother to return if the divorce was revocable, and convincing the mother to come back and accept the second wife, even if it requires her to waive some of her rights to please the father.