How could they have dealt with it better?
Any other way would have been better.
Maybe they could have liaised with the Australian Authorities to ask then to check with the women on the list later?
But dragging women out of a plane, subjecting them to barbaric searches and intimate examinations, in a car park, without any information and not a shred of consent is no way of doing it.
The baby's needs don't come into it, even if the mother had been found, it would have made no difference to the baby whatsoever.