To me the crux of this is that Rand bowed to the Crystal Throne and thus meant that the Empress could always override any order he made as his superior. So if the Empress decides the dragon's peace is over then it's over.

The fact that Tuon met the Dragon reborn before she claimed her title, so they could meet as equals, is perhaps why Rand has to 'bind' the nine moons to serve him. He doesn't need to bind anyone else into servitude as no one else sees their station as above his. (i'll be kind here and say Egwene see herself as his equal)

So, Aviendha has to do 2 things. 1) convince Rand to never bow to the Seanchan. He must work out how to bind them to him else the Aiel are lost. 2) Get to work on the Aiel PDQ. Make them see a permanent peaceful future for themselves after TG.