Hi!
I'll explain my understanding of this briefly.
Before adam sinned he was not tempted to disobey. He needed to be tempted by a third party.
After he sinned one of the things that changed was that he was now tempted from within. The sinful nature came and dwelt "in his members". This sinful nature was passed on from Adam to all his children.
Eve did not pass it on (genesis 3:15)
Jesus was born of a virgin so did not have a sinful nature. He was not tempted from within. He needed the satan to come and personnally tempt Him. This si why such a big deal is made of the temptation in the wilderness.
Also before Adam sinned he was not going to die. He could die, but he need not have.
Jesus was the same, He could die but He need not have.
We do not choose to die. We can choose when we die perhaps, but we cannot choose if we will die. Jesus chose to die...He laid it down freely.
Imagine if you were on death row for murder and another man on death row offered to die in your place. He could not substitute as he is gong to die anyway.
However if an innocent man offered to die in your place he may be able to because he would not be under the "sentence of death".
Thus Jesus realy could die in our place and undo what adam did.
more info can be found here...
http://www.custance.org/Library/SOTW/Part_III/chapter21.html
and here
http://www.custance.org/Library/Volume3/Part_VII/Chapter2.html