How do trinitarians interpret John 8:58? In John 8:58 Yeshua says:


  Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. (KJV)


If I'm not misunderstanding, and based on commentaries I've read, trinitarians believe this quote is god the son claiming to have existed from all eternity, even before Abraham.

Since the divine nature and human nature of god the son cannot be separated or divided, how did the human nature of god the son exist before Abraham?
Trinitarians do not teach that God the Son existed eternally in two natures, but that in the incarnation the divine nature assumed a human nature, and that these two cannot now be separated. This is clear in the Chalcedonian Definition, which distinguishes between the Godhead ("before the ages") and the Manhood ("the last days"):


  before the ages begotten of the Father as to the Godhead, but in the last days, the Self-same, for us and for our salvation (born) of Mary the Virgin Theotokos as to the Manhood


That the Son of God assumed (and did not have from eternity past) human nature is also clear in the Catechism of the Catholic Church:


  Taking up St. John's expression, "The Word became flesh", The Church calls "Incarnation" the fact that the Son of God assumed a human nature in order to accomplish our salvation in it. (§461)


Similar points are made in Protestant catechisms, like the Westminster Shorter Catechism, Q22.

Turning now to treatments of John 8:58 in particular, we see Methodist Adam Clarke approvingly quoting Calmet (a Catholic), saying:


  The following is a literal translation of Calmet's note on this passage: "I am from all eternity. I have existed before all ages. You consider in me only the person who speaks to you, and who has appeared to you within a particular time. But besides this human nature, which ye think ye know, there is in me a Divine and eternal nature. Both, united, subsist together in my person. Abraham knew how to distinguish them. He adored me as his God; and desired me as his Savior. He has seen me in my eternity, and he predicted my coming into the world." (source)


Similarly, Albert Barnes (Reformed) explains how John 8:58 should be understood to teach that only Christ's divine nature pre-existed the incarnation:


  The objection of the Jews was that he was not 50 years old, and could not, therefore, have seen Abraham. Jesus replied to that that he existed before Abraham. As in his human nature he was not yet 50 years old, and could not, as a man, have existed before Abraham, this declaration must be referred to another nature; and the passage proves that, while he was a man, he was also endowed with another nature existing before Abraham, and to which he applied the term (familiar to the Jews as expressive of the existence of God) I AM; and this declaration corresponds to the affirmation of John (John 1:1), that he was in the beginning with God, and was God. (source)