If the government can tell your kids what vaccinations they must receive, what's next? Can they tell parents what to feed them? Can the government mandate what TV shows kids are allowed to or must watch? Can government force kids to read certain books or attend certain functions? Where do you draw the line? Once you draw that line, why can't it be crossed or moved?
I understand the sentiment, but the major issue with vaccines, with respect to "parental choice", is that it is not a child-autonomous choice. Not vaccinating your child places others in danger. This is why we cannot have large numbers of people, children or otherwise, exempt themselves from vaccination that otherwise could receive it* without imposing a great danger to public health. Also, as a matter of fact, while we** don't mandate that children read particular books (that's religion's job), we do mandate that they, at least to a certain age, attend school - public, private, or home, so long as they are educated (again, for the betterment of society). And as a last point, we do have laws which set standards for how parents raise children; adding vaccinations to that list would not be a huge alteration of this societal notion.
* Exempting those who cannot have vaccinations for health-related reasons
** In the US