What is your objective: Are you looking for an improvement in the employee, or are you looking for a proper way to let her go?
Work-life balance is a personal responsibility and cannot be enforced by the employer. Please focus on your problems and do not try to solve her problems. I know of employees who have left their jobs to attend to parents with critical health issues full-time.
If you have already tried warnings and counseling, then please give her a clear choice between:
1. If she wants to continue in the same position (with continued responsibilities) and is ready to shift the work-life balance to work more.
2. If she wants to leave the job so the company is not affected further by her personal issues.
3. If she is ready to compromise her position, responsibilities, promotions, or increments for a certain period of time (until the recovery of her father and she can devote attention to work again). In that case, you can reduce some of her responsibilities and let her work below her capacity to retain her job and service for your company, in lieu of reduced or unchanged monetary compensation (this concept is similar to extended unpaid leaves).
The third option can provide a win-win solution, but it has to be clearly discussed based on availability and the possibility of getting deviations within your company policies.
If she insists on the first option but fails to meet your standards, then she anyway gets the third option (i.e., no recognition from the job).
If she chooses the second option, then you can hire someone to replace the responsibilities and handle them with more dedication.
Again, everybody has personal problems and different preferences for handling them. Employers or HR should not try to interfere in them. So, none of the above options are wrong or right. You can actually help her by posing clear path choices and letting her choose.
Best Regards,
Amod Bobade.