Alex was taken from Danielle soon after she was born on the Island. Danielle did not know who took her. Ben knew everything about Danielle, as he does. Ben was Alex's adopted father - and Alex knew this.
Danielle was not looking forward to a reunion with Alex, not because she didn't want to see her, but she was afraid that Alex would reject her after so many years (and after the lies she was surely told by the Others). The actual reunion worked out differently than Danielle had anticipated because Ben was there to add to credibility the fact that she was Alex's true mother. Plus, Alex was already fairly disillusioned with the Others after recent events.