While Christ has a human nature and a divine nature, they are inseperable. You cannot take away the human nature from the divine nature.
So when Christ was on the Cross, he really and truly died. But death, like it is for us, is not the end of existence, he descended into hell, broke open the gates of hell and returned to heaven where he is seated at the right hand of the father.
Then by definition, Christ, God, went to one (which one?) of the four hells? God went to hell? God died? Was killed? Then would not death be an example of mutability? Of change?
And if “While Christ has a human nature and a divine nature, they are inseperable. You cannot take away the human nature from the divine nature.”, that human nature with the divine, would have “returned to heaven where he is seated at the right hand of the father”.
That flesh and blood human nature is in heaven?
But again how can God gain (or now have a human nature in addition to the divine nature) and retain it if He is immutable?