Why was Esther not sinning when she broke the law and approached the king? Here's the text in question:


  Esther 4:15–16 (ESV)15 Then Esther told them to reply to Mordecai, 16 “Go, gather all the Jews to be found in Susa, and hold a fast on my behalf, and do not eat or drink for three days, night or day. I and my young women will also fast as you do. Then I will go to the king, though it is against the law, and if I perish, I perish.”


The commentators I have read on this passage are unanimous in praising Esther for being willing to sacrifice herself for the sake of her people.  However, they do not attempt to reconcile this praise with their statements on obedience to earthly authority.  For example, the New Bible Commentary (1970) says regarding Romans 13:


  [E]very Christian has the duty [...] to obey lawful authority so far as such obedience does not conflict with God's law or Christ's authority.


Classic examples of permissible disobedience include Acts 5:29 and Daniel 3, where followers of God are ordered to do something in direct opposition to God's law, so they disobey.  That's not Esther's situation, apparently putting her action at odds with the common interpretation of Romans 13 and similar passages.

I am looking for any Christian commentator (regardless of background) who, while affirming the infallibility of the Bible, directly addresses this apparent conflict without resorting to a "the ends justifies the means" argument.  That is, I want a commentator who either


argues that Esther sinned on the basis of Romans 13, and should not have done what she did
argues that Esther did not sin, because the king and/or the law in question are not the sort of things referred to in Romans 13
A few verses earlier, Esther states the law as such,”…any man or woman who approaches the king in the inner court without being summoned the king has but one law: that they be put to death unless the king extends the gold scepter to them and spares their lives.”  Under these circumstances, it is no stretch to say that the king, who had ultimate authority, is the judge who determines whether or not the law has been broken and punishment is meted out.  If the king had decided that she was guilty, she would have paid the penalty instantly.  On the other hand, if he extends the scepter (as he did) he is saying, “I accept her presence, the law is not compromised.”
There have been many instances where man has taken measures into his own hands to accomplish God’s work.  This was not at God’s prompting.  Mordecai’s admonition to Esther can be construed as God’s prompting and God, in keeping with his character (which He always does), would never instruct someone to sin.
I don’t know if this satisfies your question, but the way I see it we have a reasonable explanation backed up by an immutable fact.
One might also posit that we are instructed to do right or, perhaps more appropriately, Right, as in right according to God, not the local Constabulary, “Do you want to be free from fear of the one in authority? Then do what is right and you will be commended. 4 For the one in authority is God’s servant for your good. But if you do wrong, be afraid, for rulers do not bear the sword for no reason.”) Rom 13:3, 4.  A secular comparison might be federal law can trump local law.