It's been a while since I read the books, and unfortunately I don't have them all at hand to check up on. I'm not exactly a huge fan of Elayne anyways, but despite that, I think you might be being a bit unfair in a couple areas. Assuming my memory serves me correctly. In case it doesn't, I have a few questions.
First of all, did Elayne even know that Rhavin had conquered Andor from within? I seem to recall her knowing at least something about "Lord Gaebril," but I don't think she knew he was Rhavin or even truly realized he controled Andor.
Later on, Rand displaced Rhavin and took control of Andor rather suddenly. Even Graendal was caught off guard by this. (She didn't go there planning to kill Asmodean... she had intended to meet Rhavin) At what point did Elayne find out about Rand taking over? When she did find out, how long was it before she started heading for Andor? What was she doing during that time? If my memory serves me correctly, she was involved in the whole Bowl of the Winds thing (which was kind of needed for Andor and the entire world to survive), so I can forgive her for not instantly heading to Andor. But maybe I'm wrong about the timing.