Yes, Adam did disobey God by eating of the Tree of Knowledge, but it was the fruit of the Tree of Life - knowledge/wisdom, a perceptual change - which altered Adam's nature and thus caused their removal from the garden. For they had become unlike God. God did not say to not eat the fruit to test Adam's loyalty, but wisely, lovingly warned them of the potential consequence of knowing all things: "You want the Truth? You can't handle the Truth!" But lovingly.
By eating the fruit of the Tree of Life, wisdom, Adam became imbued with knowledge of their destiny, knowledge of what they were and of what was required of them to gain the eternal life they wanted. What they saw (causation) put the literal fear of God into them - Adam ran and hid and tried to cover themselves. It was fear which separated them from God, for they could not accept what they were destined to. Offered to them was the cup Jesus was sent to drink (Mark 10:38; 14:36; John 18:11), and because they (we) would not, Jesus had to.
We have in Mark 15:34 "My God, my God, why have you forsaken me?" Can you hear this loud BEEP!!? - WRONG! According to Alexander's translation from the ancient Aramaic in Story of Jesus From His Own Words, Jesus actually said, "'Eil, Eil, wherefore you left me?' In other words, 'For this you destined me'" (emphasis mine). Jesus did what Adam was unwilling to do to gain eternal life and the lordship: He ate of the Tree and STAYED. That resoluteness mattered; mattered unto resurrection and ascension - the Reward. We, in Adam's nature, are invited to join the risen Jesus in His.
By the way, there is only one Tree in Genesis 2:9, for the Tree of Life IS the Tree of Knowledge. Victor Alexander's translation of Genesis from the ancient Aramaic is the only version I know of that indicates there was only one named tree in the Garden of Eden, and that the nature of the Tree of Life was knowledge of everything (a la Wisdom in the Book of Proverbs):
2:9 "And the Lord God supplied from the earth all that is pleasing to the sight and delicious to eat and the Tree of Life in the midst of Paradise."
2:17 "And of the Tree of Knowledge of good and evil (i.e., of all things) you may not eat, because on the day you eat of it, you will die the death (death you shall die)."
3:22 "Behold, Adam wanted to be like one of Us, to know the good and the evil; now, that is why he extended his hand and took from the Tree of Life and ate, so he could live forever (to the end of the universe! Italics mine)."
3:24 "And so the Lord God ejected him, and there shot up for them from the East of the Paradise of Eden the plants of carob and a perishable life at the edge of the sword, so as there would be one day a return to the way of the Tree of
Life" (all bold emphases mine).
One might suppose "the tree of the knowledge of good and evil" in the Hebrew was a gloss added parenthetically, explaining that the tree of life and the tree of knowledge (of everything) were one and the same. A corrected Genesis 2:9 might read: "And out of the ground made the LORD God to grow every tree that is pleasant to the sight, and good for food; the tree of life also in the midst of the garden (i.e., the tree of knowledge of good and evil)." My point here is that the same tree called the Tree of Life in Genesis 2:9 and the Tree of Knowledge of good and evil there and in Genesis 2:17 is the same tree called the Tree of Life in Genesis 3:22, and 3:24. The Tree of Life imparts knowledge, as knowledge gives life. This is monumental, is it not?
'Life' has to do with causation. 'Knowledge' has to do with perception (see Bullinger Companion Bible 2:9 note). Proper perception with faith gives life! God foresaw that Adam, knowing he was but dust, could not handle perception of Adam's destiny imparted by wisdom. We, born into this world with Adam's nature, cannot, either. At least, not until we segue into Jesus' FAITH and trust in Him.
Edit: "For whereas through one human being, sin entered the universe, and through sin, death, and this death entered humanity, as [because of which] they all sinned. For until there was the Law, while sin existed in the universe, it was not considered sin, because there was no Law. Except death passed from Adam until Moses, also onto those who did not sin, as though that would become the Law of Adam, that being the death which was destined for him* (In the likeness that passes the Law of Adam, that was of the death of him that was destined)" (Romans 5:12-14 Alexander, brackets mine; see Ray Shelton).