"Your Grace"

(Grammar Questions I Couldn't Answer)

Recently my Vietnamese wife has gotten really into the historical drama "The White Princess".  (A sequel to the historical drama "The White Queen"--which I had previously reviewed on this blog).

My wife noticed that the characters frequently used "Your Grace" or "Your Highness" as a way to acknowledge the supremacy of the king or queen.  But she asked, since the intent is to show that you are acknowledging the king or queen as being superior to you, shouldn't it be "my grace" ?  As in "You are graceful to me" ?

I floated this one around the office yesterday, but nobody was able to answer it.