As an european (where in some countries, most vaccines are totally free and mandatory), I do not understand the anti vaccination movement. I am not aware if in the US, mandatory vaccines are expensive just like health care in general, and thus this could lead to think vaccination is a Pharma scam, or if it's mostly about the autism, or other unproven side effects concerns.
Vaccination is one of the biggest advances in public health, having saved billions of people, and still too many people are reluctant to it for reasons stated decades ago and based on some dubious statistics.
When you notice that more than 100 countries , even some developing countries, have higher vaccination rates than the US, you need to think if the whole world and almost the whole scientific and medical community, are wrong.

Regarding freedom, I don't know who said "your freedom ends where another person's begins" but pretty much suits this situation perfectly.

Your freedom to choose to get vaccines or not, should end when another individual can get a fatal disease due to your choice (or even spread it among many individuals). If everyone had unlimited freedom, paradoxically no one would be free.

In many countries, this kind of sentences are viewed as something positive, as these policies protect children whom are not old enough to decide on their views on matters that can directly affect their health.
Even in some European countries such as Spain, in some special cases doctors can decide to give blood transfusion on Jehova witnesses' children, going against their parents wishes, as not doing so means killing them, or letting them die (however you want to phrase it).
This goes in line with the debate on hurting a human being by non-action is or is not as morally wrong as hurting them by taking action. (Classic trolley dilemma) .