Question: Must I have my children vaccinated?

No your reasoning does not contain a fallacy, it contains a gamble. A much fuller answer would derive from game theory. For example I found this background article: Vaccination and the theory of games, but there are many others. Also in the absence of more information we are entitled to believe you are talking about standard childhood vaccinations and a standard child :-), and then your gamble has moral implications as others have pointed out. However if your school is insisting on non-standard vaccinations owing to a local outbreak of an unusual disease, or if your child has certain medical conditions, then those moral implications reduce, disappear, or even turn around the other way. Yes there is a moral dimension but no there is not a fallacy.