There are two conflicting liberties here. One for a child to be an individual and the other for a parent to be a parent.
Obviously there is a threshold at which a child is considered old enough to consent and enter contracts. There is also a requirement on the parent to provide certain basic needs (regardless of the wishes of the child).
This issue seems to me, not to fall into a basic need, but rather into the arena of consent. So the most correct answer from my viewpoint is that we may need to re-evaluate the age at which children are allowed to enter contract.
Prior to consent, a child is not free to engage in activities that would make this shot necessary. So from my perspective, it would appear that the child does have a choice (to not engage in such activities until they are at the age for which they can obtain the shot without parental approval). So the answer is, liberate children as individuals earlier so that the state does not need to intervene within families (which is a stupid idea anyway).