If it is a budget issue as much as diet, sit down with the kids and talk it over. Let them know they can have only a certain number of things each time you go grocery shopping.
For us, we do homemade pizza - with organic sauce, homemade crust, nitrate free meats, cheese, all the good stuff, just types we can handle. We never eat pizza out, we can't handle it.
We also ALWAYS keep cocoa powder on hand. One of my daughters makes whole wheat, real butter, low sugar, chocolate crisp cookies. She knows she can make those once a week, single batch. Chocolate is an approved food in our home because it helps with some of the issues with Crohn's disease. Chocolate milk and hot chocolate are treats in our home also, for the same reason.
Find special alternatives that they like. Even better if they are things they can make for themselves when they feel the need - like popcorn if they can handle the corn, or oven fries (seasoned even), chicken alfredo on whole wheat noodles, homemade thin wheat crackers (tastes like wheat thins with less sugar), etc. All of those can be made with whole or homegrown ingredients. And thin wheat crackers with cottage cheese or cream cheese is a snack that even teens usually won't turn down (we cut a package of cream cheese into 8 blocks, 1 oz each, and they know they can have one block). Peanut butter is cheaper than cream cheese, also good on thin wheat crackers, if they can handle peanut butter. You can also make your own bean dip - homemade refried beans and salsa. Guacamole is also fun and simple - just mashed avocado and salsa.
I just don't buy anything that we can't safely eat (that means pretty much no prepackaged foods at all). If my kids pig out on cake and ice-cream at a youth event, then that is their choice. I taught them not to, but they will choose anyway. They are the ones who pay for that choice. Sometimes they use their own money to buy inappropriate things also, but again, they have to learn their own lesson with that. When they move out, chances are, they'll go wild for a while and eat all the wrong stuff. But after a while, they'll go back to the good stuff because at least they will KNOW it is the good stuff, and they'll know HOW to go back to it. I've seen this pattern with most of my kids, eventually they start calling me for recipes, and asking me how to adapt things.
By restricting what is in the house, I am doing two essential things:
I am teaching them that they CAN live this way, and that it helps them feel healthier (two of them have Crohn's, so this is a big deal). I'm NOT arbitrarily forcing them to eat a certain way. I am just setting the example of buying good stuff and only good stuff.
Second, I am buying what I can afford to buy. I can't afford to buy food that is not nutritionally sound. It costs enough to buy the good stuff, I have no money to buy things that are not nutrient dense. If it isn't on the list of safe foods, I simply do not have it in the house.
I still have trouble getting the kids to eat enough vegetables. Switching from white flour to whole wheat, from white rice to brown, etc, was easy. Getting them to do veggies has been harder, especially with my son who just can't eat most kinds of veggies (he can't digest them well).
I think you need to do what you feel is in the best interest of your family. You are the mom. It is your job to lead. Buy what you can afford to buy that you feel is good. Don't buy anything else. If your kids choose to buy other things, then that is their choice - you can't control that kind of choices, nor should you try. Just keep teaching them what "good" really means, and keep setting the example by living what you preach in the home, and by NOT providing things you think are bad choices (that will just undermine your lessons - after all, if it is all that bad, why are you buying it for them).
I'd still nom them all the time if it weren't for the stupid low carb thing. *scowls*
