I don't think that they ever plan on Alex seeing her mother again... I would say that she does not even know who her real mother is... What I do wonder is who she thinks her mother is.... Or if she thinks she is part of the "research" that is going on there..

__________________
Please don't give up, Des. Because all we really need to survive is one person who truly loves us. And you have her. I will wait for
you. Always. I love you, Pen

DESMOND: I love you, Penny. I've always loved you. I'm so sorry. I love you!
PENNY: I love you too.
DESMOND: I don't know where I am, but--
PENNY: I'll find you, Des--
DESMOND: --I promise--
PENNY: --no matter what--
DESMOND: --I'll come back to you--
PENNY: --I won't give up--
BOTH: I promise. I love you.