Simple .... make it mandatory for entering children into school ... every year to have evidence that the necessary/required shots are up to date.
It was exactly this way when my children were in grade school, when we moved to Texas from Oklahoma years ago. Actually I supposed it was still in effect this way today.
If not ... why not? It was absolutely effective!
For entry into certain public institutions, a stricter policy may make sense.
But if this is for homeschooling, the policy can be laxer.