How do you cope with overwhelming emotions at work?

A little backstory:
I have been in a position of leadership at my company for about 4 years. This was the first position I've ever held with this much responsibility. About two years ago, I was faced with a series of deep personal and professional crises that culminated in my long-term relationship ending and an enduring depression that has lasted since these situations started.

Naturally, my work performance has suffered. My position is unique at my company, which is a small business, so any opportunity for an extended absence has not been an option. My company does not have the budget to retain someone of comparable skillset and me at the same time.

I have been honest with everyone about the events of my life and the toll they have taken on me personally. While on the surface everyone is supportive, I can sense frustration. I am overwhelmed easily by my emotions right now, often times "shutting down" for extended periods of time, unable to focus or think cohesively. Unfortunately, this problem is compounded by my field. I am a programmer, so I have to retain focus and clear thinking in order to complete my tasks and come up with creative solutions, which is what put me in this position of leadership in the first place.

So, how do you deal with your emotions at work and the associated stress?