I 18 years old. Do I need my father's permission to immigrate to America with my mother?

No need. 18 years old has reached adulthood and has full right to make decisions. In addition, it should be noted that even if a minor, if a party has no custody, it does not need the consent of that party.

Consent required: If you have custody, minor immigrants must get the consent of their parents who are not with you. The party with custody should write a statement agreeing to the child's immigration and sign it in front of a notary.