After finding out that Gaebril was dead and Elayne had taken the throne, the best thing Morgase could do for her realm - and her daughter - was to abdicate. Merely by being alive she rendered Elayne's claim to the throne false. It was at this point that she should have married Tallanvor and quietly gone to live on some farm in the Black Hills. Accepting service with Perrin, on the basis that she could somehow benefit Elayne by doing so, was to presume on a role and a duty she no longer had, and - as did in the end happen - it made her vulnerable to being recognised.

And in any case she should never have come back to Caemlyn, or let it be publicly known she was still alive. Elayne and Gawyn could have been told privately, and discreet arrangements could have been made to find her somewhere comfortable (and isolated) to live, with a few servants and a bit of an income. Elayne had struggled to overcome conflicts and divisions, and Morgase's mere existence could tear open those barely-healed antagonisms.