Is the wife obligated to seek divorce from her husband to appease her father, who rejects her marriage due to the incompletion of traditional wedding ceremonies?

As soon as the lawful marriage contract is concluded, you become the man's wife, and whatever is permissible for a husband to do with his wife becomes permissible for him to do with you. There is no harm in you going with him, while observing the custom regarding delaying consummation. Your father has no right to order you to seek a divorce for this reason, unless there is a valid religious justification.