The orders of the Amyrlin Seat are the orders of the Amyrlin Seat. If Gawyn has decided to abandon Elaida and serve her side, than he's expected to respect her authority, whether he likes it or not. She had given express orders to the Rebels not to organize a rescue. Gawyn and Siuan disobeyed her, and while they saved her life they truly nearly ruined her cause. If it wasn't for Elaida's capture, they might have they might have left the Rebels with no option but an attack.

I suspect Egwene as a leader was quite irritated by the fact that for all he went through Gawyn still acts like a loose cannon. He is not reliable, switch sides with the wind, abandon his responsabilities whenever it suits him and isn't in control of his emotions. He lets his feelings, not his sense of responsability or duty determine his choices, and whether to obey or not orders. In terms of fighting skills he's a near perfect warder, but he doesn't have yet the maturity for the job. As a lover, Egwene is more forgiving and must be pleased with his courage and his love etc., but as Amyrlin, she can't approve of Gawyn's behaviour and actions. She loves him, but if he's to be her warder, he needs to change.

Egwene was a bit like this back in LOC - a loose cannon who didn't understand self-control and the importance of orders and rules, but she's grown up a lot lately. She's irritated Gawyn has not. Bryne, who trained him as a boy, thinks much the same of him, incidentally.