Sorry to hear that you're having a tough week, but I'm happy to see you taking an accounting of the positives in your life, as well. Yin and yang. Things are just slightly out of balance, but completely recoverable.

Dealing with employees, whether as an owner or supervisor, can be a challenge. What can help is taking the emotion out of the equation when disciplining or otherwise dealing with an issue. For example..

I'd tell the employee that you value her and both appreciate and depend upon her reliability. That you've come to understand that she's working at a competing gym and you're trying to find out both why that is, and how it can be best resolved for both of you.

Are you sure she knows it's a conflict to work for both? If she has access to client information, your gym's financial information, or other important data that you're looking to protect, then I'd lay that out for her calmly and deliberately so she understands why this dual employment can't continue. If she doesn't, then is it really a conflict?

I'd also suggest breaking the issue down into two, separate conversations. The first being fact gathering. The second, the next day, the resolution. This affords both of you an opportunity to reflect on what you've both learned and to make an informed and seasoned decision as to how to proceed...

Hope this helps, my friend...