No employer can simply terminate the services of an employee without observing the due process of law pertaining to disciplining misconducts just because at times s/he fails to obey the instructions of the superior. Similarly, just to avoid unpleasantness, the employer can not insist on immediate resignation.
If the performance of the employee is good, she can be given proper counselling to mend her behavior towards her superiors and to follow the procedural formalities relating to her work to the satisfaction of the superior.
Instead, if you feel based on her past record that she is not amenable to counselling or the like, frame specific charges against her, conduct a domestic enquiry by affording her all reasonable opportunity and then terminate her by means of a speaking order.
6th August 2019 From India, Salem