If God is omnipresent, or exists everywhere at once, does this mean that He is present in hell? How can the wicked be sent away from God's presence if God is present everywhere, including hell?

God Is Everywhere Present

One of the attributes of God is that He is everywhere present. The psalmist wrote.

Where can I go from Your Spirit? Where can I flee from Your presence? If I go up to the heavens, You are there; if I make my bed in the depths, You are there. If I rise on the wings of the dawn, if I settle on the far side of the sea, even there Your hand will guide me, Your right hand will hold me fast. If I say, "Surely the darkness will hide me and the light become night around me," even the darkness will not be dark to You; the night will shine like the day, for darkness is as light to You (Psa 139:7-12).

The idea that God is everywhere present is a biblical doctrine.

Wrath Present

How then can God be present in hell - a place where Scripture says is separate from God? God will be present in hell in the sense of His wrath. Hell is the place where God's wrath is expressed toward unbelievers. The writer to the Hebrews said.

For indeed our God is a consuming fire (Hbr 12:29).

Attempting to Flee

In the Book of Revelation we read of people attempting to flee from the wrath of God.

They called to the mountains and the rocks, "Fall on us and hide us from the face of Him who sits on the throne and from the wrath of the Lamb!" (Rev 6:16).

Of course they cannot succeed in running away from God's presence.

Summary

Heaven is where God exists. In heaven He demonstrates His love toward His creation. Those in hell are indeed banished from God's presence although God is present in hell in the sense of His wrath. There is no love in hell.