I liked a lot of those Amador chapters, especially the growing respect and even affection between her and Pedron Niall (I really miss Niall; for all his faults it seems like he was the one decent and halfway wise Captain Commander). It also provided a convenient intro for full scale unambiguous Seanchan re-invasion. Anyway....

Morgase had few options, and none of them good; the one thing she (rightly) decided she could NOT do was stay anywhere in Andor, waiting for Rahvin to send out search parties to swoop her up and restore her as his figurehead. Beyond that things become difficult, as she also realized at the time; she could seek sanctuary as a relative of the Damodreds by marriage, but that opens the door for them to try using her in some convoluted plot to gain the Andoran throne, the Cairheinin, or both. Murandy was a disaster area even before the Dragon was Reborn and unlikely to change; Ghaeldan wasn't much better. Most of the west coast was under Seanchan control that was only increasing (though non-existence intelligence and "fog of Rahvin" probably meant she didn't know much of what happened after Falme or she'd have never gone to Amadicia). Rahvin had already turned her against the Tower, so the otherwise best and most natural option was also off the table. That pretty much leaves the Borderlands, Tear or Illian by default. I'd probably have headed to the Borderlands and hoped their respect for women and my title would prevent me being raped in the street, or forceably married to the first overambitious lord who found me, or his son. Probably her best bet would've been to go try to seduce King Paitar of Arafel, though it seems doubtful that would've worked. Let's not forget though, Rahvin was surprised she retained enough conscious thought to even manage escape, so just getting to Amador was a major accomplishment.