Contact that employee and tell her that after sleeping on it, you realize that you didn’t treat her the way she deserves to be treated. You can explain what you were thinking at the time, but keep that short and maybe skip it completely. Just apologize and thank her for what she’s done for your team.

Then tell her that you are going to honor her request of staying with the company through the week. Explain that she doesn’t have to come in to work, but that you’re going to keep her on the payroll through Friday.

Then wish her well with her new job, and offer whatever explanations or mea culpas are necessary for HR to make this happen.

If you do this, the employee will feel like you and the company treated her right (more than right), and word will spread to your team that you’re a good leader who is willing to admit (and fix) mistakes. This actually generates more loyalty than if you hadn’t ever made a mistake in the first place.