I think the fact they took clothing and other items point to the baby being cared for and a possible good ending to this case. If they were covering up a crime scene...there was no need to remove the extra items mentioned if they were kept inside drawers, etc. (unless there was evidence on them).
The mother is certainly the POI in this case. The grandmother cannot be overlooked either as she could have helped stage this before she picked up the father. Are there TWO grandmothers in this scenario? Was it the maternal or paternal grandmother picking up the father?
If I were in Iraq and the mother was not sending me photos of the baby I had never met...I would be livid and calling LE for a wellcheck of my child! Surely, he has more recent pictures of this baby!!