We need some sort of legal construct that would hold those who do not vaccinate responsible if there is an outbreak in the area. For example, you don't vaccinate your daughter for whooping cough and my daughter(too young to vaccinate) catches it. My daughter has to suffer months of terrible pain and discomfort in addition to potential long-term consequences. I should be able to seek compensation from you.
Of course there are other social alternatives, such as lychings.
As a side note, you probably don't know shit about vaccines. What makes you think spacing them out will improve her reactions to them?