Happy? Aim lower. How about making it through the day. One step at a time. Don’t over think it or think you can will your way out of this. You can’t. If you could you’d be better or managing already. Take a step. Btw, I have two kids as well. They are great but don’t make things easier or better necessarily. Focusing on yourself is the best thing you can do for them.

I suggest you to try CBT. The therapist won't try to tell you why you should be happy or why are you worthy, the treatment is different. You can try CBT, or ACT (acceptance and commitment therapy), or perhaps also a rogerian therapy can be of help.

CBT didn't work for me. But more conventional therapy did. Everybody is different and that is exactly why professional help is so important, depression is a common condition and there are lots of different treatments. With the right treatment you will get better. I did. Thousands of others do too.

I would recommend finding a therapist. I was in a similar position as you and therapy helped me a lot. Hope you get better.