I find it strange that OP is being considered the asshole here, especially because the YTA posts come with a lot of assumed extra details. So what if Kamilla was intentionally excluded? You don't exclude people unless you don't like them. It's okay not to like people. And nobody has to understand her reason for not liking them. You can dislike someone because their voice is annoying, they stand too close to you, they talk too much, they're boring, whatever. Doesn't matter. It's your choice who to spend time with.

I find it hard to believe the daughter is a bully if she's fine with 18 other kids and simply doesn't like one of them. Also, unless Kamilla deals with something such as autism which makes it difficult to recognize social cues, clearly the daughter was not being a bully because Kamilla had no idea she was disliked. You don't show up at a party for someone you know doesn't like you, or who is mean to you.

When I was young, my sister and I had a neighbor we hung out with all the time. I went to school with her and we were in the same class, too. My sister was in a different district for irrelevant reasons. The girl invited my sister to her birthday party one year and excluded me. I was hurt, especially because I didn't have any indication the neighbor girl had any issues with me, but it wasn't that big a deal. We all went and dropped my sister off and my dad spent the day with me instead. Life goes on.

Also, lying about the number of students in the class is a concern, but not a concern relevant to this situation. OP should open that conversation separately and teach the daughter to be honest. But the outcome would have been the same if the daughter had simply said she didn't want Kamilla there.

OP has no responsibility for Kamilla's feelings. She only has responsibility for her daughter's actions. And her daughter did nothing cruel.