It sounds like your daughter sees them as friends much more than they do her. They aren't wrong for planning things without her, and it could well be that they'd never really consider that it's something she would feel particularly left out by, if she's not in their friendship group, so don't have a problem mentioning it to her.
I've been part of groups as a child and an adult, where you are friendly with all the people in the group, sometimes share lifts, maybe even occasionally do things with, but it's a relationship from being part of the shared activity. Some within that group would have much closer relationships with each other as well. Occasionally I've been part of a closer friendship within that, but usually I'm on the outside. And of course those groups do other things and talk about them even when part of the bigger group. Yes, it can hurt to feel that I'm not part of that when I might wish I was, but equally, I feel no entitlement to be included - just wanting to be included doesn't mean that they are being mean by not including me, or vice versa. I very often was lonely and looking for friends, so those groups seemed more attractive to me and I was more desperate to be involved, whereas others had more friends of their own outside it and didn't care whether they were part of those little groups or not. I doubt the people in the smaller groups would have known who might have minded and who didn't. The problem comes when someone assumes that they are close to some of the others or part of an established group, when really they aren't seen that way by those in the group.
And that might be what your DD is experiencing. She might want to be close to them, they might not dislike her, but they may not feel she is particularly close. It doesn't mean they won't respond to her invitations, but they don't have to include her. You can just stop inviting them if you don't feel it's reciprocal enough.
As adults, we meet people that we aren't specially bothered by, maybe mildly irritated by something they do or just not that interested, but don't dislike for any reason. Should we refuse any invitations that they offer, because we don't intend to become closer friends? Some people might think so, but I doubt most people do. They don't mind staying as friendly but not super-close acquaintances. Would you be less hurt if they rejected all the offers of lifts and activities with your DD, because they didn't see her as a really close friend? That sounds more hurtful to me.
OP goes on about how she always thinks of other people's feelings and can't imagine hurting anyone the way they've done, but I'm not sure letting a child invite herself where she isn't specially wanted is thinking about those people's feelings either. It's putting them in an awkward position, it's potentially spoiling a party they'd planning by having a changed dynamic that includes someone they aren't close to, it's making things awkward between a child and parent, etc. Your DD probably won't actually feel any less hurt by someone having to include her and going along to the party - it's the finding out that you're not close to someone you thought you were that hurts, however it's done. She will have to keep looking for friends that suit her more - these friends haven't necessarily done anything wrong by not wanting to be close to her (though they might be being mean for the sake of it - but you don't know that). They might just not like her all that much and don't feel close to her. Your DD can keep trying to find other friends that really do click with her, whilst still being on friendly terms with others. If you think that she is being socially awkward - the fact that she's still inviting herself along at age 12 suggests she doesn't really understand unspoken rules that well - maybe there are other social skills that she's lacking too. Or maybe they just don't like her loads, which is sad for her, but doesn't mean they are wrong. There will be other people who do, though, if she just doesn't click with them.