It is funny that I haven't written about the Trinity in quite some time on this particular thread!!! If you go back, I think it has been several weeks! Before I continue, I will start by saying that discussing the Trinity is fraught with difficulty, as we have only seen the slightest of light in the subject. This, like the Incarnation or the Eucharist, is a subject that we can only go so far. Our rational thought will not be able to grasp these concepts completely. With that said, let's see what's going on here.
You said "...They are in perfect agreement 100% of the time."
Yes. There is only one divine will. Each possesses the totality of the attributes of God, and each possess the will. They do not share it. Again, a difficult concept to grasp. But without this, we fall into the problems of trithesism.
You said "...Because Jesus Christ chose to leave eternity and enter our time domain, He layed aside His Omnipresence."
I think it would be better to say that Jesus chose not to use it. If you say He layed it aside, He no longer has the divine nature, correct? Then He is "only" Jesus the man. A good analogy (if you noticed, I like analogies) would be the following. The person of Jesus Christ is like a mountain, covered with clouds. Only the peak of the mountain pokes through the clouds. This portion represents Jesus divine knowledge. It has access to the light. The portion below the clouds represents Jesus in those moments when He "does not know the end time". Or when He is suffering on the cross. His humanity does not have access to the "light" during these moments. Yet, the person of Jesus, through His divinity, does. During His sufferings, Jesus did not have access to the light of His divinity - but there is no separation.
If we say that Jesus' divinity left Him during His sufferings, we are becoming docetists, the Gnostic heresy that John fought. They said that Jesus' divinity only appeared to suffer, or that His divinity left Him during the suffering on the cross. This goes against the Apostolic Tradition and the Scripture that somehow, Jesus the person suffered - which continued to include both the divine and human nature. If His divine nature left Him, what good would His suffering had been then, as it would not have been perfect. Only God can offer a perfect sacrifice.
Regards
The unholiness was lain on Jesus' flesh and soul, not His spirit where His divinity exists. This is why He could show us that His fleshly will must be submitted to the Fathers will, and that His fleshly will may be different from His Fathers will. Never once did He act out on His fleshly will, there fore He was legitimately tempted in all points, yet remained sinless.
The three only ever existing persons -- Father, Son and Holy Spirit -- have a loving relationship that we won't know the intensity of until we are in heaven.