Is that right then user that not finishing an exam is all the proof required to secure extra time?
no, its part of it, you need a lot of evidence, including samples of work, and statements from teachers, etc
Why should she cram them in around lessons when she has already completed the wrong exams once why were they the wrong exams? Do you mean they weren't the ones you wanted her to do! That doesn't mean the school didn't want her to do them though, and if not, why didn't she say so before all the exams were finished? It sounds like these others are an option that she is being allowed, but it wouldn't be right for her to miss lessons because of it, and you also have very little flexibility as to when someone is available to invigilate.
but she does need the extra time and a room away from the the exam hall and her TA in attendance.
she won't be allowed her TA in a public exam, noone adult who has been present in the lessons is allowed in the exam hall, or to see the exam paper until AFTER it has been sent to the exam board. Normally 2-3 days.
She will be allowed to be in a separate room, but many of these separate rooms are filled with quite noisy and disruptive pupils, such as those on word processors, speaking to scribes, allowed to take breaks, etc.