Apparently not. Before the bureaucracy engaged in coercion, women took 15x more parental leave than men (according to the article).
I'm also curious why you feel that being cared for by the father rather than the mother will cause the children to be better adjusted. Are women so much worse as parents than men?
Your example of immunization is a separate issue - not being immunized creates a harmful externality. Having an unequal distribution of parental leave does not.