I am so sorry you are experience this level of depression. I understand how debilitating it feels. It is especially terrible when, as you said, there's really nothing wrong.
Could it be there's really nothing right, instead? Just a different way to look at the issue in hopes for realization or an epiphany. It works for me sometimes.

I know it must be hard feeling like you are letting your kids down. I can't relate because I don't have children, but I understand. How old are your kids? Are they old enough to understand mental health issues such as depression and the symptoms they come along with?
It could be a good talk to have with them if they are old enough because there could be more understanding from both sides. Maybe you're not letting them down. Maybe you and your kids can use each other for support during the darkness of this time.

I hope you begin to find some relief. Let me know if you'd like to talk about anything. PM me anytime.