....she didn't work for the union, she worked for the School.
Then how was she in the union? Did the union get dues? If so, how? If they were a third party, they'd have no power to do that. It's only by being the outsourcer and owning a guaranteed monopoly contract on labour that they can do what they do.
Due were voluntary. After a few years she disagreed with how the union was doing things so she left the union, aka, stopped paying dues. it's a weird setup for sure.
Oh, weird. Was it REALLY a union then? Sounds more like a club or group of some sort. Maybe you can have a real union like that, but how does it work if it is voluntary? I mean, that's great, but it's weird for sure.
You are oversimplifying union shops. They take many forms. Some are mandatory, others are not. In some places you negotiate your own contract if you are not a member. In others you get the same contract as the union members whether you join or not. The list of permutations goes on.