I think it was helpful that Danielle had her daughter, niece and mother to look after, that that helped her move on. I doubt she would have left Europe and stopped searching for her son, given her conviction he was still alive, if she hadn't been motivated to care for them.
And I also think she was very self-possessed and confident in her abilities to overcome difficult situations. When tragedy strikes it can be very easy to simply stop caring about life and a lot of people would have caved. Danielle, however, decided she needed to step up and not succumb to her sorrow. Not everyone would have been able to do that.