(long time reader, first time poster, hey everyone!)
I'm thinking they probably didn't keep Alex on Alcatraz very well, seeing as she had a boat. What other reason would she have a boat other than to go between islands? And if she can do that, perhaps she's even met her mom (or one of her mom's traps). We also know that Alex is capable of making her own trap-type devices (the trap door hiding place), which could also hint that she knows her mom somewhat and was trained by her.
But if she's seen her mom recently at all, there'd be no reason to go kidnapping Claire's baby. So I guess I'm stumped.