Hi TTBE
You should have a conversation with the cemetery office where your father's funeral is taking place and alert them to this situation and also the officiant, I don't know whether this will be a priest, vicar or celebrant. But apart from asking the person not to attend as their presence would cause more upset at an already difficult time, there isn't much you can do.
During burials, the officiant will invite people around the grave to come forwards to pay their final respects and at this point flowers can be put into the grave along with the coffin. This would give the person mentioned the opportunity to do what you do not wish to happen.
There is also the possibility that after the family have left the burial, the person mentioned remains behind or comes back another time and puts ashes on top of the plot after it has been filled in. Unfortunately, once the cemetery gates are open, the staff there can't monitor every plot and you can't sit there day in and out to watch either.
I hope our replies have helped you to deal with this a bit better, a problem shared is a problem halved so they say, and by mentioning your problem to a group of unrelated people this might help you in some way and give you some ideas as to how to move forward.