It is my (unconfirmed) understanding that at least here in Canada, the body of a deceased person belongs to the next of kin. Even requests for disposition of the body in a will won't necessarily guarantee the wishes of the deceased, since it's not unusual for a will to be consulted until after the funeral. However unless all members of the family are in agreement to go against the wishes of the deceased, trouble will certainly be in store. In my opinion, it isn't good to go against the wishes of the deceased without a valid reason.
Just to clarify: I do support the Orthodox stand on respectful treatment of the body after death, including burial.
Trevor, during your father's catechumenate, you should try to find a gentle way to be sure that these matters are included in his studies.