What is our legal right in this situation?
Know the difference between insubordination, gross insubordination and insolence
There's a fine line between insubordination, gross insubordination and insolence of an employee.
Do you know the difference? How would you discipline an employee in each instance? If you get it wrong you could lose at the CCMA!
The simple truth: You can't simply dismiss a sick employee
There's no simple, quick solution I'm afraid. You must handle an employee that suffers from this type of illness through the incapacity procedure due to ill health.
You have to go through a counselling process. You also need to go through a formal enquiry about this and the negative effect it has on you, her manager and her colleagues.
Terminating her employment through a disciplinary procedure will be dangerous, especially since you know about her Bipolar diagnosis.
You need to think about her ability to do her work, the fact that her ill health is permanent, if you can adapt her work to fit her need and the availability of alternative employment - which you've already said you can't do.
Only after you have done a complete investigation, and seen that termination is the only option, can you give her notice and terminate the employment agreement.
This is a long process, so don't think it will be a quick and easy solution.