The comment about the half-sister also being a bridesmaid says a lot. It shows that the OP doesn’t think her sister’s father’s family should feature in the wedding and totally disregards the fact they are her family. That’s something the Op has probably got from her mother and father. It’s very telling
I think this sums it up for me. I agree it's very telling that OP's criticisms are all focused on her sister's choice of having her dad's family involved.
OP, I invite you to be really, really honest here. Can you honestly say that there have been no attempts to airbrush your sister's dad's family out of the picture? How much of your sister's dad's family's sporadic contact was their choice, and how much was it down to your parents pushing it away?
Your choice of language when writing about your sister is revealing more than you think. You say your sister and your dad "get on", which doesn't sound like the best of relationships to me. Did your dad assume he would automatically be walking her down the aisle? Just because he's step dad?
You've been lucky by being able to grow up with both parents, and now you are getting upset because your sister isn't doing what you think she should be doing.
Maybe you should talk to your sister, without judgement, and really see how growing up in your household was for her. You might be surprised at what you hear.