I too offer my sincere condolences. For someone to cause additional upset at such a difficult time is inexcusable.
I do hope that explaining yours & your mothers wishes is enough to deter this person, but if not it will be very difficult for them to scatter ashes into the grave unobtrusively unless they are carrying them loose in their pocket, which is unlikely.
At my mother's burial the cemetery workers were stood a respectful distance away but still close by, so you could perhaps notify the cemetery in advance and ask them to quietly step in front of anyone who tries to open a bag, jar, box etc near the graveside. Not ideal, I know, but better than you or a family member having to deal with it.
if your fathers grave is then covered immediately after the service, which I believe is normal, this would remove any opportunity to add anything after the service.
But if the very worst happens and the ashes are scattered, remember that they will not remain there. Wind, rain and nature will take care of that, and it will be your mother, and only your mother, who will rest by your father when the time comes.