At the risk of also sounding like a dinosaur, what do a 12 and 16 year old need data on their phones for? pr0n?
Data is the most expensive element of a phone plan these days...if they need a phone for emergencies, a $10/month prepaid plans should be plenty.
Good call on the car...ditch it, especially since you already have alternate means of getting to work. If you sell the car, I would maybe not buy a car until you've achieved a certain amount of debt reduction (i.e. 50% of existing non-mortgage debt)...sort of like "until I get rid of 50% of my debt, I won't have a car." Your means of transportation for all basic needs are all covered (going to work and school). You'll survive, and it will motivate you to pay down that debt.
Food has been covered...pretty much a combination of what everybody else is saying. If the kids want to bring a lunch to school, have them make their own. If they want to buy lunch at school, then they should be using their own money.
Is the haircut expense for you? Not too sure how the female body works, but I think my wife cuts her hair once or twice a year. I think haircare for the husband and the two boys needs to be at $0/month right now; buy a set of clippers and clip away.
What is softener?
Honestly, if you didn't have the debt, your expenses really wouldn't be that bad; your household income is high enough that you wouldn't need to fine tune absolutely everything in your budget.
Focus on getting rid of the non-mortgage debt. Throw everything that's leftover at it.
I don't think you're in bad shape at all, good luck.