It's not necessarily that what they're doing is wrong, but rather that the presentation is hypocritical. It's not much of a difference between Elayne or Colavaere seizing the Sun Throne. In fact, Colavaere did this a fair while ago, Elayne does it at the eve of the Last Battle. If order in Cairhien was the goal, then wouldn't an established monarch with months to prepare be better than one with only days?

Cairhien would have fought in the Last Battle anyway. They've been fighting for Rand going on months now. That wouldn't suddenly change. And frankly, the idea of the Shadow invading Andor through Cairhien if that country falls is pretty silly because both their armies - Andoran and Cairhienin - should be fighting further north anyway. If Trollocs get to Cairhien or Andor, then neither country should really have the forces to stop them anyway.

And what about the part where she wanted to start a war with the Two Rivers because despite the fact that Andor hasn't ruled it in generations, maps still claim that area as part of Andor? Starting a war with one of the Light's champions as the Shadow grips the land, because of what? Morgase said that the Two Rivers hasn't seen a tax collector in generations, but Elayne sent one. What changed? The fact that it was suddenly prosperous? The fact that it could now be used to increase Elayne's power and influence?