I mean if they knew about the end of the Earth and were just wanting to take some kids away to start a new world why did they bother leaving those codes for people to decipher?
What was the point when all they wanted was to save children?
... those codes were a kind of calling, it appears. although, I would agree that a more straight-forward way would have worked out better, though it would have lacked the tension for a movie.
they needed to find the children that "got" the message and it took time to track them (given that some hadnt been born yet) - so it was a case of those who heard the message were drawn to the right place at the right time - that was my interpretation.
But the message was psychic. Although it was indicated rather indirectly, and only at the end, Abby must have been hearing the aliens talking for some time. If the aliens want and can trace receptive children, why bother to stand at their doors for weeks, or send cryptic messages to their grandmothers? Why not simply collect them directly when the time comes. And don't bother with cars either.