Hmmm... I see this is a week old, so maybe you don't need any more comments. But it's actually very easy for this kind of thing to happen, I think - mainly because you have a child is doing something which is anomalous, and not in the 'proper' timetable. If you have nearly 2000 pupils, each of whom has a slightly different set of subjects, and each of whom needs a particular pattern of setting (eg high in MFL but low in Maths), then it's only a false click of the mouse in the timetabling software to get them accidentally in the wrong set, or attending at the wrong time. Remember that in a school that size, you'd probably have something like 1000 different sets in 15-30 different subjects over 5-7 yeargroups.
Usually schools get this right, and in a way I'm surprised how well it works, when you consider the amount of information that has to be processed in a short period of time. But when there are mistakes, you rely on a teacher or pupil spotting it - like the boy who said his maths was too easy. That particular example you give doesn't worry me at all - obviously, it's not great that he was put initially in the wrong set but in itself it doesn't indicate a systemic problem. Tbh, I don't think it sheds any light on your dd's situation.
As for your dd, I am appalled that it has taken 6 weeks of teaching for this to be properly addressed, but I can see how this might happen as a series of small, compounding errors rather than any single enormous failure. She is on an unusual programme of activities - from what you say, one that the school hasn't implemented before. Therefore they probably don't have the systems in place that would be able to process her activities easily (the software for this stuff is extremely complex, and often is not well adapted for one-off, individual activities, and she obviously wouldn't fit into any pre-existing paper system either). You seem to suggest (did I get it right?) that she turned up to some things and was told she was in the wrong place. The individual teacher would have no way of knowing where she should go - they would no doubt have expected a Year 9 pupil to ask someone about this (form tutor? HoY? Head of relevant department? Director of Studies?), as they would not be in a position to know where she should actually be.
If she were not turning up to something she was officially timetabled for, then that really is a big problem - huge duty of care issues. That's worth a great big complaint. However, if her activity was off the standard timetable this is less surprising. Almost inevitably, the school's usual system of producing registers etc would not work for this activity (unless they are really unusually well organised - this stuff is a real headache to manage in most cases), so it would only need one more administrative slip on an ad hoc arrangement for this not to be noticed. Of course, it shouldn't happen. You are absolutely right to be upset about what was (at the very least) a series of small errors with very big educational consequences. But in a huge, complex system, a unique arrangement for a single pupil can go missing without revealing a systemic problem.
The thing is that in any school, the fail-safe for this kind of error is that the pupil will notice something is wrong, and will ask why they have no scheduled English lessons or whatever. It's not clear to me whether your dd did this and was fobbed off (v v bad) or whether she just went to the library and there was some sort of miscommunication and she stayed under the radar because no-one properly understood there was a problem. By saying that, I don't want to excuse the school - your dd shouldn't have been in that position. But to me the unusual thing about this is not the nature of the mistake, but the failure to pick up on it.
To my mind the issue this raises is one to do with Learning Support and pastoral care. Clearly the mistakes were in academic administration, and they need a rap on the knuckles; but the mistakes might have been relatively small, and regardless of size would have been picked up very quickly if the pastoral care (eg communication between your dd and form tutor) had been working properly; or perhaps if Learning Support had been doing a better job of overseeing her (from what you say she would be well known to them, and they would have some responsibility for general oversight of her progress). In your letter, I would be focussing on this aspect, rather than the timetable one.