I'm virtually certain that the mother in this case is a photojournalist who previously worked for Al Jazeera. Her website (now defunct) is archived
here. It includes links to social media profiles that are still online, though not updated in years; the woman in the Facebook photos is almost definitely the same person in the police handout. She goes by the nickname Toots and has other children (presumably they're safe and accounted for). It looks like Mark Gordon could be the father of the older kids as well as the missing newborn.
I'd usually expect these kinds of details to be in a missing-persons story, but the information in the media and police statements has been scanty. Something feels very odd here.