What is the ruling on someone who, intending to travel for Hajj, performs 'Umrah on behalf of his mother and Hajj on behalf of his father in one year, then reverses the intention in the following year, performing Hajj on behalf of his mother and 'Umrah on behalf of his father? Is this permissible?

Hajj and Umrah are two independent rituals. The Prophet, peace and blessings be upon him, clarified how to perform them in the forms of Qiran (combining them), Ifrad (performing Hajj alone), and Tamattu' (performing Umrah then Hajj). So, whoever wishes to enter into Ihram for Umrah on behalf of his mother, then for Hajj on behalf of his father after exiting Ihram, may do so, or vice versa. It is also permissible for one to enter into Ihram for one of the two rituals on their own behalf, then for the other ritual on behalf of someone else after exiting Ihram, because "actions are by intentions."