Hey man, I don't know the solution, I too live with the constant thought of not really wanting to live on the backburner in my mind too, it is very incessant, for a long time after my separation I really did feel like things were getting better, I had coped with the loss of my ex - I am a year and a half out, and life is stagnant right now, and despite the intuition that has never failed me and that I have grown to trust, screaming at me silently that there is no purpose for me, I am pushing to fight through it and flip those thoughts, flip what my instinct is telling me about my self-worth, because there is a part of me that still has hope in this world that it will not be a complete waste.
One thing I am coming to accept, the thing that has always disturbed me about people saying "you owe your children a mentally healthy father who doesn't take the cowardly way out" is that is just a fear tactic, as mean as this sounds, I don't want to live purely to provide for my son, I want to live for me. And one thing I have resolved in my mind, based from a comment I read on this site last year (by whom I can not remember) is that before I even come close to offing myself I would make a genuine effort to go for broke - if you are constantly thinking of quietly oozing down the drain of the deceased why not instead do something crazy and spectacular that you think is good and someone should do in this world? one thing about getting your mind to a point of having nothing to lose is that you become free to try something full of all kinds of risk that would have held you back before. I don't know what that is for you, but maybe you go backpacking across south america, climb a building and yell something to the world, I don't know just do something other than closing your eyes forever.
And if you can't bring yourself to that point realize that what is holding you back is that you do in fact have something to lose, so recognize that and make a proactive choice, take ownership of that choice so that you can start making your life what you want to. Your marriage may be dead, so what? The damage to your family has been done, and you are not the one to take all the blame, you get less than half the blame - so no longer dwell on it because you can't change it all you can change is your attitude, and when you begin getting the right attitude (which is what I am trying to work on in myself) good things will come into your life again, fatherhood becomes sweeter, days become brighter and life becomes more peaceful.
I don't really want to preach advise, I just want you to know as unique as your feelings are to you, you are not completely alone in them. I sense your pain, If you need to say anything I check my inbox here all the time, PM me anytime you need someone to listen.