If God is a perfect God who cannot be in the presence of sin because He is so holy, then how can He be an omnipresent God if there is all kinds of sin going on in the world and if there is a hell?
Good question! God cannot look WITH FAVOR upon sin and evil, but He can certainly be in the presence of sinners. This is proven by God’s omnipresence (as you noted), the incarnation of God the Son, and even God’s continued (if temporary) interaction with some of the fallen angels (including Satan – e.g. Job 1-2, etc.).
The limitation is not on God. Sometimes we have this image of God as needing to back off from sin and evil because He can’t allow Himself to be in its presence (rather like Superman avoiding Kryptonite because it weakens him?!). But we would suggest it’s more like the reaction of mold in the presence of bleach, or of anything combustible in the presence of fire: God’s holiness is so consuming and so purifying that unless He restrains Himself (and that only for a time), nothing impure and unholy can remain in HIS presence. It affects the creature, not God.
Hope this clears things up a bit.