IMHO, she needs to not give a rat's hiney what the Aruban's think of her. She needs to be herself. Who cares what they think? Or what we think, for that matter. This woman is on a mission to bring her daughter home and will not stop until it's done. The quickest way the Arubans can get rid of her is to help her find her daughter so she can leave and get out of their hair.
Besides all that, if she doesn't do this, she'll fall apart. This is her coping mechanism. The woman literally has no choice if she wants to keep herself together long enough to help find Natalee.
Actually, believe it or not, you DO have a choice; you can get in bed and pull the covers up over your head and fall off the edge of the earth, or you can live your life in a way that reflects the values and character your child believes you represent.
It's a conscious choice. And she's made it.