If I were still a practicing ob-gyn and one of my patients said she was not going to vaccinate her child, I might try to persuade her to change her mind. But, if I were unsuccessful, I would respect her decision. I certainly would not lobby the government to pass a law mandating that children be vaccinated even if the childrens parents object. Sadly, the recent panic over the outbreak of measles has led many Americans, including some self-styled libertarians, to call for giving government new powers to force all children to be vaccinated.
http://www.ronpaulinstitute.org/archives/featured-articles/2015/february/08/vaccine-controversy-shows-why-we-need-markets-not-mandates/