Does the dad have court orders/ consent orders? A parenting plan? What sort of access does he currently have?
Look, it might not be a bad idea to book mediation with relationships Australia. He can tell her that it is an opportunity to work together to be better parents for the child by getting some assistance to help discuss matters of concern. If he gets to mediation, they will hopefully help the mum understand that she can't make these sorts of stipulations, and if she chooses to withhold the child it will not look good in court.