I believe there are strong grounds for compulsory vaccination in public schools, and would support a government's decision to do so. Although I think a parent should have the greatest influence on the way their child is treated medically, when their decision has the potential to impact on the health of others it becomes a public, not personal health issue.
Although it is not the role of government to legislate the well-being / parenting of children, where there is any potential risk of public harm, this risk does become an important consideration and compulsory vaccination would be a relevant action for the government to take. As the managing authority of public schools, and of public health, I believe that the potential risks associated with an under-vaccinated population are too great to be ignored. The government must consider the potential impacts a non-vaccinated child can have on the population (given that vaccination is not 100% effective and a vaccinated child may still be affected by a non-vaccinated one).
At the same time I acknowledge that this is a difficult issue that places any government in a tricky situation of weighing up the public good dividend achieved by legislating something that is for the most part a parent's right to choose. However this is increasingly being done with safety laws (e.g. pool fences, car seats) and these are not public but personal safety issues.
I assume that with any government decision, it is backed up by rigorous scientific consensus - i.e. there is broad (albeit not unanimous) scientific opinion that the links between vaccination and eg. autism are tenuous at best. Personally I don't believe in the arguments against vaccination presented by the conscientious objectors - the doctor that linked MMR to autism in the UK has been widely discredited and I believe is not allowed to practice.
I also think it's important that compulsory vaccination does not completely divorce parents of control of their child's upbringing, as it does still provide parents with the option of not attending the public school system and also not vaccinating their child.
I think this was a very good answer. Well done
One thing I would go further in is discussing briefly the impact that one parent's decision to not vaccinate their child has on another. ie how ethical is a parent's decision to not vaccinate their child and put others at risk? Do they have an ethical responsibility as a member of society as well as that of a parent? Further isn't it hypocritical to demand having the right to not vaccinate when that very action puts another at risk? Are you allowed to demand a right that takes away someone else's right?
Again not entirely necessary, but if you did go down that ethical road, I'm sure you'd get bonus points