Take the whole vaccination-germ thing out of the equation and read your own post: You want her there because YOU go to her kids' events and you threw her a baby shower. So...you threw her a shower expecting that she would reciprocate by coming to a social event of yours? Not because you happen to like her?
That's how it sounds.
It sounds like you base your friendship with her on keeping score: You did X for her so she now must repay you by doing Y.
If you consider yourself close friends with her...what's the friendship based on, really? If you were good friends with similiar interests, etc., beyond just both having young kids, then I think this tit-for-tat scorekeeping would not matter to you, but it does, so it sounds as if you are really just all about keeping things "even" between you. That's no basis for a friendship between adults. Or even between kids.