You can't blame the social workers when someone up-sticks and moves without registering elsewhere. Seems strange to have moved away from her family support network in Kirkcaldy, maybe she moved to Edinburgh to get more work.
Is it as straightforward as that, John? Surely in a case where a child's welfare was being severely compromised, authorities would want to keep in regular contact with the family and would note the fact that the they had disappeared from the radar. Wouldn't that in itself be a cause for concern?
It is possible that the mother moved to Edinburgh for a job - or for a less innocent reason.
It seems significant to me that this woman appeared to have taken a very different direction in life from her middle-class, educated parents, as had the guy she was having a relationship with before he was killed earlier this year. He was the son of a prominent religious community leader (muslim) at the large mosque in Edinburgh, yet seemed to frequent the pubs and clubs and worse, eventually being shot to death in gang warfare.
Both of them seemed to have taken a bad turn in life. She presents herself on social media as quite a flippant, irresponsible person despite all the pictures of the kids. Something must have happened in her life that set it on such a different and unfortunate course.