Is it permissible for someone who traveled for Hajj to intend ‘Umrah on behalf of his mother and Hajj on behalf of his father in one year, then reverse it the following year by intending Hajj on behalf of his mother and ‘Umrah on behalf of his father?

Both Hajj and Umrah are independent rituals. It is permissible to enter into ihram for Umrah on behalf of one person and for Hajj on behalf of another, or to enter into ihram for one of the rituals on behalf of oneself and the other on behalf of someone else, based on the Prophet's (peace and blessings be upon him) saying: "Deeds are by intentions, and every person will have what he intended."