Actually, Elizabeth goes after Will because she loves him. 😉 Remember, her concern is that by leaving Port Royal behind, she is leaving Will behind. "A fair trial for Will ends in death!" Also, she tells her father that Will is a better man than he gives him credit for, and that they should wait for Will because he has gone to get Jack.
No where does she say that Jack needs to be saved. They don't know that Jack is in trouble.
Remember? Governor Swann explains to her that Beckett never intends to grant Will, Elizabeth or Norrington pardons...that the only one available is for Jack Sparrow. Therefore, when she steals the letters, it's because she now knows that Beckett is NOT going to grant Will a pardon. It has nothing to do with her lack of trust in Will.
So she is a wanted criminal who has escaped from jail AND has stolen from the head of the EITC. So what's she going to do? She leaves to go find Will.
Also, what you are telling me is a theory, not a fact necessarily. There are plenty of rumors that disprove what you've just said. You can, of course, believe what you want, but to me, we won't know anything for sure until the movie is released. I don't believe for one moment that we have the entire story already, seeing as there are almost daily revisions on the script and I don't believe they are finished filming yet.
So anyway....back to the topic. Will becomes a lot craftier by the second film. He played DJ pretty well, I thought. It was quite...piratey if I do say so. 😉