At what age is a birthday party the child's instead of the parents'?

It should always be about them, not the parents. For the first and possibly the second birthday, its understandable to invite only family friends, because those are the people who care the most about the child, then, as soon as the child begins making friends, they should be invited along with a few of the closest adults who really care about the child, like godparents, close family friends, etc. It should never be friends who are just the parents friends and really couldnt care about the child. With my kids, for their first couple birthdays it was just family friends and family, but they were all close friends who cared about the child, they werent there for me, then when they were three and started socializing more and started preschool we invited their preschool friends. I think that you should remind your sister that this is her childs birthday, not hers, on her birthday she can invite her friends, but this is her childs birthday and should be centered around them, including their friends, not her friends and their older kids who are only there for the cake and because their parents said they had to.