Ah, well, there is much to work with here:
the Navy's head can be persuaded his wife's death was somehow a plot, a murder or something, and create false leads that frame the dictator as responsible for her death somehow.
the Navy's head can be played by an inserted agent that would make sure to subtly feed his depression to the point of insanity or suicide. This can be achieved by planting subtle reminders of his wife all around him, or planting forged personal documents or evidence that would create an impression the wife was miserable in the marriage, didn't love him or betrayed him before her death, or that he was somehow responsible for her death. (It all depends how she died)
the minister of FA can be exposed, of course, which would create scandal. it can even be used to discredit him while other allegations would be planted that create the impression that the demonized FA minister is conspiring against the country with his lover who is a leader of neighboring country. The neighboring country can be accused of secretly planning to overtake the dictator's country and he can even be blamed to be part of the conspiracy, planning to sell his people.
The minister of FA can be extorted quietly, since he's so afraid, he can be made to betray the dictator by giving information about him, or sabotage or even assassination.
These are just some options off the top of my head.