Is there dualism in God?

In a word, no.

There can't be. If God is all-powerful, all-knowing, all-present, there can be no separation at all. There can be no distinct parts, features, preferences, mannerisms, traits, or characteristics in a perfect god.

I mean, fantasize with me for a while. Imagine we are in Heaven paying a visit to God. The first question that comes up is, which God are we visiting? The God of Earth? The God of some other planet? I think most people (excepting LDS) would say, "Well, there's only ONE God!" The LDS doctrine is that there are many gods. This doctrine creates many problems and questions because of the inherent separation in a belief in a plurality of gods. Are all the gods equal? If so, why do we need more than one? Are they each all-powerful? Do they compete? Do they compare 'notes?' Do they compare their works to those of other gods? Do they argue? Do they have private thoughts and private activities?  How can privacy even exist in a realm of omniscience?

So back to our fantasy. Let's leave the LDS doctrine and go with the one espoused by most Christian religions: there is only One God, the God of all the universe. Let's go visit Him. Or Her? Does god have gender? A body? An appearance? A presence? Does god have moods? Preferences? Habits? Hobbies? Does God have time for a visit? Or is he too busy answering prayers and creating stuff? Does God have to maintain things after he creates them? Does God have to intervene in the affairs of his creations? Or does he intervene just for fun? Does God mess with us? Or does everything he does have a divine purpose? Does God intend only good? Does anything ever happen that God didn't intend?

And we could go on and on. Some parts seem pretty silly. But, to a person who tries to impose dualism on God, the only answer you're left with to these (and many other) questions will ultimately be, "We just are not capable of understanding all the ways of God."