@jolly-homestead In the U.S., the easiest route, instead of getting into debates with the medical monopoly theorists, is having a spiritual exemption. I have written out and signed a number of them for friends.
However, for your children, the most cogent way to explain vaccines is: "One cannot induce health into a living organism by injecting with a septic matter." The human body is such that giving the body stuff that it produces causes an interferance in that production rhythm and the body will attenuate the supply. Vaccines interfere with the body's natural immune system.