Just jumping in.
I agree with others that it sounds like you don't need to buy anything, with all the house stuff you have bought lately. And go cash/envelope - if you can get it where you are, Gail Vaz Oxlade's show Til Debt Do Us Part (HGTV) shows lots of examples of families in your boat, and how to do proper budgets and pay down debt. She also had couples do activities together and figure out how they got into their messes and how to get out, so they may serve as examples for you and your wife.
Your wife has 2 jobs right now - the kids, since she is a SAHM, and CE/FO - that is chief executive/financial officer for the family company of Beatles Inc. She (and you of course) needs to pinch every penny until it screams. Cost analysis on everything that does need to be bought - which right now is food and utilities. Food - nutrition per unit cost. Do your kids like the pre-flavoured single-serve instant oatmeal packages? Gone. Buy oatmeal in bulk. And don't buy the fast-cooking unless it its the best buy per serving. Cold cereals are a total rip-off, they are mostly air, and don't fill kids up. Gone. Everything others have mentioned, plus - laundry - cold water washes. Clothes that need dry-cleaning, stop wearing them so the dry-cleaning bill goes away. House - turn the thermostat down. Hot water is expensive, cut back. Phones - you have cell phones, do you also have a land line? If yes, do you need it? If yes, cut it back to basic services. Cancel magazine/newspaper subscriptions and read them at the library - same for books. Subscriptions, if you have prepaid ask for a refund on the unused portion. No booze. I mean it, not only is it expensive, but it relaxes you and you waste your evenings vegging.
Your pie chart was basically useless as a guide to future practice, not enough information. You can't do any of these cost analyses until you look back at your previous spending, so you really need to do that detailed breakdown now. (I just saw your post, that you have posted - good).
And for what it's worth, I have seen families in more trouble than you are on Till debt do us part, so I don't think you are trolling.