Rand sent his messenger through with a gateway. He followed later. Why do you assume that Graendal knew that Rand was close to her Palace with the Choedan Kal?

It's a HUGE error in logic. Firstly you assume she knows that Rand is around, when he mentioned that he was going after Graendal at the very moment he actually went, so it was impossible for her to know. Secondly, it's outrageous to think she'd know he had the Choedan Kal on him at the time.

The chapter is not vague. If Graendal was going to flee then she would have Compelled the messenger and left, sensing that Rand might be getting close. For all she knew he'd sent a messenger to every noble house in the area, and hers was one of many. There is no way Graendal knew that Rand had just popped up and suddenly planned an overly elaborate plan to make her Compulsion unravel at the exact moment that he completely unexpectedly balefired the Palace with the Choedan Kal. For crying in a bucket, even Min and Nynaeve didn't know what was happening, and they are his allies!