Softly-softly approach when staff won't teach
The allocation of teachers to classes is a part of the headteacher's responsibility and it is clearly unacceptable to have a situation where teachers can refuse to carry out their assignments. If they do so, the onus is on them to demonstrate that the head's direction is unreasonable. The grievance procedure exists to enable cases to be tested.
This formal statement of the case does not really address your situation, because you are dealing with a teacher who is almost certainly very stressed, as well as with a particularly intractable class. Given the measures that you have already taen to support the teacher, albeit unsuccessfully, and assuming that there are no more feasible ideas, the hard line of simply directing her to get on with the job runs the risk of the union claiming that you are refusing to acknowledge a serious case of stress. At the same time, you do not wish to convey a message to an unruly class that they have got rid of a teacher, or to other staff complaining about a class.
The resolution of this situation can only be reached as a result of serious discussion with your senior management team and with all concerned parties. It may be that this is a case where a judicious exchange of classes, covered by a carefully-prepared cover story, would be the best negotiated solution.
Questions should be sent to Helpline, The TES, 66-68 East Smithfield, London E1W 1BW