you are going to keep working on your processes and setting expectations, but if she was good, she would be coming up with methods and processes that will help her preform better. And help your company be better, lighten your workload, etc.
Speaking from experience of keeping an underperforming/bad employee around longer than I should have, it's better when they are gone and replaced.
I was afraid how I would manage if I let that person go so I kept justifying to myself that she was doing better. She wasn't and when I finally did fire her I was able to see more clearly that she wasn't a good employee, even though I liked her as a person.
Once I got a different person who really did do a good job in that position, I wondered why I drug out firing the first girl so long.