It's not in the best interest of other children to let your children not be immunized.
One of the reasons immunizations work so well is because of herd immunity. The entire population doesn't need to be inoculated against every random mutation the virus will take. Enough of the population has good enough immunity that the virus can't take a foothold. But once you dip below a certain percentage, the virus gets free rein to spread and evolve again.
Effective immunization requires that we all mostly get immunized.