I have read many of your posts isleguy and i read your BW's post. I think you 2 are much like me and my WH and we have many similarities regarding our marital history. I could go on and on regarding how our stories are similar but in this post I'd like to share with you what i believe you could do to help your wife.
--- give her a weekend with NC by sending her to a hotel/friends house for a weekend getaway. Plan it all for her and give her the details along with a letter stating that you have decided to finally commit to change 100%...that upon her arrival home, you will be a changed man. Express your feelings and your hopes and your DEEP remorse for how you have destroyed her. Then plan activities youre going to do with the kids but leave room to have the house clean and everything prepped for the workweek.
--- upon her arrival home you stay consistent and you carry the "joy" of the household. You are optimistic and rigidly consistent with reading, reflecting and sharing. You anticipate and respond to her triggers. You offer support emotionally about day to day issues and A related issues. You are complimentary to her about her looks, her accomplishments, etc.
---you journal 3-4x/week about what you're learning, what realizations you have, how you feel differently now versus in the past. You make this journal available to your BW. Read books and articles about your specific areas that need growth and self improvememt. As others mentioned, decide who you want to be and figure out how to get there.
--- you continue to offer support in the household duties and child care. Let your wife see you really bonding with the children....as a group and individually. Plan activites with just you and the kids every 3 weeks or so and offer her alone time during that period.
--- develop or refine your transparency plan. How will you ensure she is comfortable during these times where she is not with you....when shes having alone time and when youre doing stuff with the kids?
--- expect that there will be times when she explodes. Dont be defensive; recognize and validate her pain amd emotions. Apologize specifically for what anger she is spewing. DO NOT get stuck in shame. Respond to her bitterness and the little jabs she takes by showing LOVE and remorse and do not defend.
---schedule weekly conversation time with your wife. Be prepared to discuss insights you have gained through reading and reflecting.
Schedule date nights at least monthly. (This is separate from her alone time). Date nights will be tricky at first. Ask for date nights to be free from in-depth A-related talk but do not think this means you shouldn't respond to her triggers...and of course try to pick non-triggery date night activites. (Almost everything is a trigger because you systematically "attacked" from all angles. Be aware of her mood and emotions, apologize and tell how you thought then versus how you think now).
---consistency IS THE KEY!! You have said it time and time again....you are lazy. You have lacked the consistency that is needed to get the 2 of you out of this long, painful, maddening cycle.
Decide to commit to 100% from this day forward. I get it...4 kids, jobs, houseowrk, bills, car repairs, school functions....it's tiring. You have to decide that your wife is REALLY your priority. Think of ways to help you stay on task...maybe a calendar that allows you to plan the kid functions, her alone time, date nights. You could track your journal entry schedule and progress with reading on there also. Think of a mantra or maybe use a picture that will help spur you when youre tempted to not do what you know you should do. She will not believe in this "change" for quite some time and that is understandable because you have failed at being consistent time and time again. Be consistent!! Since you 2 have been stuck in this cycle so long i believe it will take extreme willpower for you to push through her pain and anger but the consistency is what will do it. Be Consistent!!
In case i haven't mentioned it...BE CONSISTENT!