Realistically, there are times when people die and others are relived that their toxic influence is gone.
But it's different with your children. They are still young. They are attached to you and love you, in spite of your self-destructive and potentially other-destructive actions, because at that age, you are an integral part of their foundations, for better or worse, and it will rip away the foundation before they are prepared, and before they have the capacity to effectively recover. They do not yet have the cognitive or emotional capacity to manage your abandonment via suicide.
They are not yet old enough nor have enough emotional foundations to be so sick of your actions that they feel empowered and freed, assuming that you are not violent and verbally abusive, spewing your problems and utter vitriol onto others to discharge it; even then, there may be enough love and enough good that they will be terribly conflicted, as are most children of any kind of abuser who also shows some love and does some supportive things. If you are an abuser, you can stop. You can contact a domestic violence center and ask for referrals to services for helping offenders, not that you necessarily are one, but so that you don't become one. I think you see that your addiction-based actions do offend, and you need support for that. I'm not sure where you will find it, this is but one suggestion, and it is up to you to seek resources that you sense will benefit. This is part of building your own strength, backbone, and foundation.
If you choose to suicide and enact it, your children will wonder, as children do, what was it about them that caused you do to what you did, or what did they lack so that you wouldn't stay. They will feel responsible for and therefore punished by your act, even though that is not your intention, and they may or may not eventually be able to place the responsibility on you it where it belongs, because it is your choice and not theirs, by your will and not their influence. They will likely believe that they had influence, because it is likely impossible for them to grasp at this age that they have no control over you, your actions, or their own situations.
They will have to deal with other children and adults knowing what you did, talking about it, judging you, and, as cruel children will, judging, blaming, and tormenting them for having been abandoned, for having a father who hated them so much that he killed himself. This is what children and the Greek chorus of an ignorant society do.
This will be a far worse and more painful interruption of their lives than anything you're doing now. They may not have the strongest foundations that are of necessity built on your own which also is not strong, as well as your wife's, but you are still a foundation, and they already rely on you to be present. They will feel punished and blown off course by your self-chosen death, even though your intentions are the exact opposite.
This is no pro-life guilt trip. This is a wider perspective of the far-reaching impact of your choice, and I recognize that's a skill that has been challenging for you to develop. I am speaking straight, but there is also a lot of compassion. I get that you are often tested beyond your capacity to manage. Yet you have made steps in recovery, you do have skills that you didn't have before, and you can continue to take new steps forward. As others have said here, relapse is often a part of recovery; you can feel defeated by it, or you can use it as a guide to point out where you still lack tools and resources, and seek them out, seek to continue the difficult progress, and gain more strength, confidence, power, and rewards -- maybe not the rewards you seek such as work and money, but foundational rewards that help you manage the ever-changing fortunes of life. You can, as @Living sucks mentioned, find others to talk to who will give you good advice and help you start to see the path, the pitfalls, and how you may stray toward hazards rather than running from them. They will not do it for you, but they will give you tools, like corrective lenses for visual impairment, hearing aids for auditory impairment, or walking sticks to help you (re)learn balance.
There is a fine line between being co-dependent and giving others control, and then resenting them when they don't let you stray, vs. having someone in your life who is solid in themselves, who doesn't try to control you or take on owning your shit nor your successes, but such people do exist, the people who give tools but don't force you to use them, or try to step in and use them for you. It is up to you as part of your self-ownership and self-determination to seek out these people and support, and to keep going if you don't quickly or easily find them, which is far more difficult and yet far more powerful, I think, then the self-determined choice to end your life when it will cause so much more destruction than anything I think, based on your posts, that you're doing now. Such people will help you find your inner power, your will power, because you do have it. I don't know how many bullshit messages and past experiences it's buried under, but it's there.
I have one suggestion for you. Offer empowerment and de-enmeshment to your wife, and then drop it, let her do with it as she wishes or not. Offer her the suggestion of going to Al-Anon and/or CODA, and then stay completely out of it. It's up to her whether or not to do so, but I guarantee that she is enmeshed in this and needs to do her own healing and find her own power. She, too, needs foundations so that she doesn't rely on you when you are not capable of being reliable, nor try to cure you, control you, or own any cause for your problems. You each take on too much ownership of the other's stuff, and give ownership of your own stuff to each other. I'm not a mind-reader, but this is how such relationships work.
You can keep beating yourself up, calling yourself selfish, self-centered, a failure in your role, and a living breathing piece of shit, which all feed the flames of your tormenting hell in order to falsely validate that it is hell and should function as such. It is the ultimate place of condemnation, and as long as you are functioning from such a place and giving it credence, you will not believe that you can heal, that you are worthy, and that you are anything more than a pathetic, hopeless, not-even-demon piece of shit who only stinks things up and has no hope except for flushing. You're not an angel, either, and so you won't become one. You are human, and there is imperfect but powerful grace in the world available you to help you out of that fake pit, because the world needs humans who strive to become ever more aware and to do better; that's not utopia, but it's imo the best kind of world in one full of imperfect humans who will always be imperfect, but can strive to grow and do better if they so choose. It needs people who are reciprocal, who use gifts well, who give good gifts back when they are capable, and who become an example for others who also think they're in hell. Such examples exist for you, I hope that you will seek them out. They are imperfect humans, too, and helping you when they have the power and detachment from your issues will help them as well. It will give them meaning and purpose, it will help them to stay on their paths, too.
I also offer you the tools of Brené Brown's talks and interviews.
That's all I've got to offer without stepping into fixing. I can't own your stuff, I can't convince you, I can't push you if you don't want to be pushed, so I won't push. I've offered you the best gifts that I could, and I have no control over whether you recognize them as such, choose to receive them, or choose to employ anything in them which can serve you. That's not because I'm cold, quite the opposite, but because I'm not co-dependent; I'm both autonomous and caring, and I've shown caring without taking on unwarranted burdens of responsibility for things over which I have no power anyway. I have enough burdens of my own, I would not dump them on you, and I do not seek reciprocity or assistance, you have enough to deal with, which I have recognized and shown that I care about. And so I have done my imperfect but heartfelt best to give you support, such as you tools if you choose to use them, akin to a rough map and help stations along the terrain. It is up to you whether you want to be on a path or in the rough on that terrain, or if you want to be on the journey at all, and if so, it's up to you how you want to try to travel it.
I sincerely wish you and all whom you love the best for your well-being and freedom from suffering and from old delusions that keep you unjustifiably trapped and tortured. I wish you only the best support, and the best inner and external resources to face the challenges of your life which you did not initially cause and which I declare have no more right to control you, but ultimately it is up to you to declare, as it is your life.
I wish for your personal power, and that of your wife, and for your children to be able to build the abilities to develop their own personal power. You may regret that you had them, but you have them; it is up to you to determine your influence, as you cannot escape from influencing them, in life nor in death. You can move forward if you choose to, and at this point of crisis you will as crisis demands a change of direction, either toward new solutions and support, or toward self-elimination, whether passively through addictions or through total and permanent destruction. I do not own that choice, but I sincerely wish you the best in determining your choices, and I do not judge what you do, because I am not you, and I have no control over you -- nor would I want it. I neither condemn nor forgive any choice you make, because I do not have that power. But I also won't sit back and watch with popcorn nor digging my nails into my seat. I have used my power to the best of my ability to serve you, and I recognize your autonomy and right to do whatever you choose, however you choose to. And so it is best I withdraw with only the best wishes for you, and with trust that you don't yet have that you've got this. If you don't, I know that you have been trying. You wouldn't be posting if you weren't, so I think there is something that you've got. I respect you and I honor you. Every word I've written is a product of and reflection of that.
I leave you with these words from one of the only flawed humans to have ever inspired me and given me the kind of valuable guidance I've suggested you seek from others. These words inspired how I have spoken here to you:
If any person is able to convince me and show me that I do not think or act rightly, I will gladly change; for I seek the truth, by which no person was ever injured*. But they are injured who abide in their error and ignorance.
- Marcus Aurelius
I do not wish to see you injured, hence I spoke.
*only their other-serving filters are injured, which do not belong