I am so sorry you are feeling so bad. Currently though, I don't think you are a bad father, none of those reasons makes you a bad father. You go through with this, then yeh, you are. I have seen some very messed up people who lost parents to suicide, and to do that, knowing you are probably going to mess your children up makes you a bad father.
HOWEVER, right now you are not a bad father, and you still have a choice, you can choose whether or not to be a bad father, or a good father.
Which is it you want to be?
There will be free support groups around, maybe you could look into them. You could find there are ones for single fathers, or people going through divorces, or those with depression, or whatever. Maybe you could pick up drumming again, it might give you a positive outlet for what you feel.
I don't doubt you are in unbearable pain, but suicide is not your only option, not by a long shot.
You posted this thread, and then said you didn't want to be talked out of it. Can I ask why you posted the thread? What you felt the point of it was? What you wanted from it? I'm glad you did post, but I just want to make sure of what you wanted from the thread.
Please keep talking.