no you're assuming that the mother knows the woman who took her.
If I were to be arrested and arrangements made for DH to pick DS3 up that any one of his friends (or friends of his friends) could walk into the police station pretending to be him and take him. I know a couple of his friends, but not the "wider circle".
If several phone calls have been made then it's quite concievable that "news" has travelled and someone that doesn't know the mother has turned up to get the child.
And is better that she's with someone she knows (presuming that she does know her) - I would say no. Victoria Climbe knew the people she was with, as did that poor girl who went "missing" and was found under a bed in a (relatives?) house not far from home.