Is God present in Hell?
It is one thing to talk about God's choosing not to be present somewhere. If He ever chose not to be present in any particular place, then He wouldn't be inherently, infinitely, and eternally omnipresent.
The problem with hell is not that God isn't there. People often think that hell is the absence of God. Everybody who is in hell would do everything that they could to get rid of Him. They would pay any price if it was possible. The problem is that He is there, and He's there in His judgment.