Fortunately I don't think we've yet had a situation where forced vaccinations for children really were, medically, unsound.
A child is not entirely the parent's property nor does the parent (in practice, let's disregard a utopian idea on the differing question of what one might want to be the case) entirely have all rights regarding decisions for the welfare of the child, and it's long been recognized or considered that other parties can step in when health decisions made by the parents are bad. So it is not so clear-cut there.
For example, most people would agree that if it were a fact that if a child did not receive a medical procedure, the child would die, whereas if he or she does, the child will do absolutely fine and the parents refuse, it is appropriate for a doctor to administer the procedure anyway.
I do dislike forced or nearly-forced vaccinations for adults, though, who should have the say regarding their health.
For example, I have had the flu exactly one time in my life, at age 8. Regardless of many exposures, often rather thorough exposures, to people quite sick with the flu. I therefore personally conclude that I have high natural immunity to the flu.
I therefore do not want this shot.
But as an example of nearly-forced (not that actually-forced may not occur), when as an adult, over age 30 in fact, wishing to attend the University of Florida as a long-standing Florida taxpayer, I was required to receive various injections that I do not at all believe I needed and would not have chosen. One or two were IMO useful: I did have use for the tetanus booster. Maybe one other, can't recall.
But that is an example of how the government can "nearly-force" medical procedures on adults. A next step could be being unable to renew your driver's license if you don't provide proof of immunization. After all, "driving is a privilege not a right," we are taught to parrot.